physics  Lib. 

Q.C 

Zl 

<S92n 


THE  NEW  SGIENC 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


APR  2 2 1863 


THE  NEW  SCIENCE 

THE 

FUNDAMENTAL  PHYSICS 


BY 

W.  W.  STRONG,  PH.  D. 


THE  NEW  SCIENCE 


OF 


THE  FUNDAMENTAL  PHYSICS 


BY 
W.  W.  STRONG,  B.  S.,  PH.  D. 


S.  I.  E.  M.  CO. 

MECHANICSBURG,  PA.,  U.  S.  A. 
1918 


COPYRIGHTED,  1918,  BY  W.  W.  STRONG 

(All  rights  reserved) 


Library 

c 
2.1 


Q 


This  work  is  dedicated  to  two  whose  love  has  been  as  true  as  nature,  the 
inspiration  of  my  life,  the  fondest  treasure  of  my  memories,  and  the  founda- 
tion of  the  hope  that  these  loves  are  the  earnest  of  the  great  transformation 
to  a  love  unbound  by  fate  and  a  truth  unfettered  by  ignorance. 

The  blessings  of  such  unselfish  love  inspires  this,  my  credo  of  life: 

I  believe  in  the  intelligible  ordering  of  all  phenomena  by  a  Good  and 
Supreme  Being  in  whose  image  we  are  privileged  to  understand  and  direct 
His  creations. 

I  believe  in  the  most  perfect  philosophy  of  the  world  and  of  life  that  we 
can  devise  as  the  guide  for  ourselves  and  our  organizations  so  that  the 
heritage  of  the  Past  and  the  works  of  the  present  will  bring  most  directly 
the  Great  Democracy  of  Truth  and  Love  to  all  men. 

And  I  dedicate  the  full  striving  of  my  heart  and  mind  to  the  gaining  and 
giving  of  the  Truth  and  Love  of  my  Heavenly  Father  to  men  with  the  full 
Faith  that  we  here  prepare  for  that  most  glorious  transformation  to  the  per- 
fect ordering  of  our  perpetual  Homeland  with  our  Father  and  our  brethren. 


118830G 


The  author  wishes  to  record  that  the  formation  of  the  Research  Corpora- 
tion by  Dr.  F.  G.  Cottrell  appears  as  an  important  step  toward  the  time 
when  the  ambitions  and  dreams  of  our  youth  will  be  for  knowledge  and 
truth  and  the  employment  of  wealth  will  be  for  the  realization  of  all  those 
visions  that  experience  intimates  will  be  for  the  uplift  of  all. 


vii 


PREFACE 

There  has  been  in  the  writer's  and  there  is  probably  among  all 
of  us  an  intense  longing  for  the  fundamentals  in  life.  Busy  as 
we  may  be  with  the  common  details  and  tragedies  of  existence, 
there  are  times  when  we  contemplate  a  much  more  enduring 
scheme  of  living  and  thinking  than  that  which  now  guides  or 
rules  us.  The  college  student  sometimes  elects  his  subjects 
with  reference  to  what  he  is  lead  to  believe  is  of  fundamental 
value  in  so  far  as  he  can  judge.  A  very  few  people  direct  the 
energy  and  the  enthusiasm  of  their  lives  along  carefully  planned 
channels  in  which  they  believe  the  most  fundamental  and  valu- 
able results  will  be  obtained.  For  the  great  unthinking  majority 
it  is  as  in  politics,  every  man  always  votes  for  the  best  candidate 
and  so  as  regards  the  fundamentals  of  our  philosophy  of  ex- 
perience and  of  living  most  of  us  vote  right. 

The  unsophisticated  might  be  awed  into  believing  that  surely 
the  pages  of  our  select  journals  and  books  of  science  written  by 
the  inspired  disciples  direct  from  the  research  fields  of  nature, 
would  contain  in  them  part  of  the  real  philosopher's  stone;  and 
this  I  sincerely  believe  is  true.  Those  of  us  that  have  been  in 
those  fields  of  research  also  know  that  they  are  indeed  stony — 
stony  even  unto  becoming  a  wilderness  of  doubt;  and  that  while 
sojourning  there  we  must  subsist  upon  the  manna  of  our  opti- 
mism, else  the  promised  fundamentals  beyond  the  Jordan  become 
clouded  by  the  fleshpots  of  our  Egypt  of  selfish,  "  what's  the  use" 
philosophy,  and  that  we  may  still  be  in  pursuit  of  the  funda- 
mentals when  every  citizen  possesses  a  heart  enriched  by  the 
experiences  of  Gethsemane,  and  whose  mind  has  been  trained 
by  years  of  fruitful  research  in  the  fields  of  knowledge. 

But  were  all  goals  to  be  achieved  only  Nirvana  would  remain, 
and  our  optimism  is  to  be  measured  by  the  progress  that  is 
being  made,  rather  than  pessimism  as  regards  the  reaching 
of  the  absolute.  Surely  the  recent  discoveries  and  the  visions 
given  us  by  the  new  Science  inspire  a  most  unbounded  optimism, 
that  yet  greater  progress  is  to  come. 


x  PREFACE 

There  is  arising  among  the  sciences  and  in  technology  many 
new  developments  that  foretell  a  new  natural  philosophy  or 
outlook  upon  knowledge  that  promises  to  greatly  clarify  and 
simplify  knowledge.  We  appear  to  be  in  the  midst  of  a  period 
of  a  revival  of  knowledge  as  well  as  of  the  humanities,  steps  of 
which  have  been  marked  by  the  new  geometries  and  the  principle 
of  relativity. 

Events  appear  to  hold  the  promise  that  the  concentrated  efforts 
of  peoples  to  win  in  a  war  will  be  replaced  by  a  more  unified 
aim  to  know  life  and  nature  and  to  apply  this  knowledge  more 
fully  to  the  service  of  man.  The  following  essay  is  the  writer's 
bit  in  a  movement  which  he  hopes  will  eventually  provide  every 
man  and  every  organization  with  the  most  advanced  and  well- 
ordered  program  for  the  direction  of  their  efforts. 

W.  W.  S. 

500  S.  YORK  ST.,  MECHANICSBURG,  PA. 
March  8-June  7,  1918. 


CONTENTS 

PAGE 

Dedication v 

Preface ix 

Contents " xi 

4.  The  Goal  of  the  New  Science 1 

5.  The  Disappearance  and  Conservation  of  Energy,  Electric  Charge 

and  Mass 6 

6.  lonization  Phenomena 13 

7.  The  Gateways  of  Knowledge  and  the  Growth  of  Science 23 

8.  Some  Problems  in  Physics 31 

9.  The  Directed  Elements 34 

10.  The  Entity  Systems  of  the  Universe 38 

11.  The  Atomic  Structure  of  Matter  and  the  Equipartition  of  Energy 

in  the  Newtonian  World 43 

12.  The  Disintegration  of  Atoms  by  Radioactivity  and  the  Nature  of 

Our  System  of  Matter  Elements 49 

13.  Some  Models  of  Atoms  and  Atomic  Nuclei 54 

14.  The  Ritzian  Atom,  the  Magneton  and  the  Neutron 62 

15.  The  Corpuscular  Theory  of  Light 68 

16.  Huyghens'  Secondary  Wavelet  Centers 69 

17.  Electric  Lines  of  Force 70 

18.  The  Electromagnetic  Theory  of  Radiation,  the  Theory  of  Gravi- 

tation and  the  Equipartition  of  Energy 72 

19.  The  Electric  Nature  of  the  Ether,  the  Hypothesis  of  Electroethons 

and  Radions 78 

20.  Some  of  the  Universal  Constants  of  Nature 81 

21.  The  Fundamental  Definitions  and  Units  and  the  Ceer  Theory.    .  84 

22.  The  Etementarquanta  Theory. 93 

23.  The  Relativity  Theory -, 100 


4.  THE  GOAL  OF  THE  NEW  SCIENCE 

The  outline  of  the  older  natural  philosophy  is  quite  well 
exemplified  by  the  contents  of  the  ordinary  textbooks  of  physics. 
In  quite  separate  divisions  there  are  treated  mechanics  and  the 
properties  of  matter,  kinematics,  dynamics,  gases,  liquids  and 
solids;  heat,  wave  motion  and  sound,  light,  magnetism  and  elec~ 
tricity.  In  a  similar  fashion  the  different  sciences  and  branches 
of  engineering  are  separated  from  each  other  on  account  of  the 
way  that  they  have  developed  historically  and  it  has  only  been 
quite  recently  that  a  new  science  has  arisen  from  a  critical  ex- 
amination of  the  groundwork  of  the  sciences. 

This  new  science  is  essentially  a  more  complete  application  of 
laboratory  methods  to  the  basic  units,  measurements  and  laws 
of  science.  It  aims  to  apply  the  empirical  method  and  eventu- 
ally the  same  method,  units  and  apparatus  to  all  phenomena. 
The  new  science  is  essentially  a  philosophy  of  the  laboratory  and 
aims  for  the  universal  extension  of  the  experimental  method.  It 
states  that  no  term  or  theory  of  the  natural  world  possesses  any 
meaning  unless  it  is  usable  in  the  laboratory.  Such  terms  as 
time,  length,  direction  and  mass  must  be  definable  in  terms  of 
experiences  of  the  natural  world  and  unless  they  can  be  so  defined 
in  a  given  region  of  experience  they  possess  no  meaning  there, 
fundamental  though  these  terms  may  appear  to  be. 

Philosophically  the  view  that  the  world  consisted  of  the  four 
elements,  water,  fire,  earth  and  air  would  be  quite  convenient 
and  comprehensive  for  the  Greeks.  In  Plato's  time  some  could 
consistently  believe  that  everything  is  explained  by  motion  or 
that  all  is  rest.  For  a  large  group  of  phenomena  the  phlogiston 
theory  is  ample  and  probably  no  theory  appeared  so  complete  to 
some  minds  as  the  vortex  ether  theory  of  the  atoms.  The  past 
philosophies  of  phenomena  have  been  quite  fruitful  and  if  we 
change  their  phraseology  they  bear  a  remarkable  likeness  to  the 
theories  of  today.  Call  the  four  Greek  elements  solids,  liquids, 
gases  and  energy:  speak  of  the  motion  theory  as  the  kinetic  theory 
of  gases  and  liquids:  adopt  the  theory  of  a  stagnant  ether;  change 

1 


2  FUNDAMENTAL  PHYSICS 

phlogiston  to  energy :  and  view  the  atoms  as  consisting  of  rings  of 
electrons  rotating  about  the  nucleus  of  the  atom  and  we  perceive 
a  remarkable  similarity  of  ideas. 

The  workers  of  the  new  science  aim  to  develop  as  simple  and 
as  comprehensive  a  philosophy  of  phenomena  as  did  the  workers 
in  the  past.  But  they  are  devising  a  system  and  a  laboratory 
method  best  suited  for  the  study  of  phenomena  as  the  first  step 
in  the  problem  and  as  the  investigations  continue  the  very  fun- 
damental]elements  of  the  experimental  system  employed  are  to  be 
modified  so  as  to  further  these  investigations.  As  a  concrete 
problem  let  us  consider  the  motion  of  an  alpha  particle  (which 
consists  of  a  helium  atom  carrying  a  double  positive  unit  of  elec- 
trical charge)  with  a  velocity  of  120,000  miles  a  second.  The 
collisions  of  this  particle  with  other  particles  of  matter  is  entirely 
different  from  those  we  are  familiar  with  when  lower  velocities 
are  concerned.  This  alpha  particle  will  pass  through  all  of  an 
atom  except  a  very  minute  portion  called  the  nucleus  and  it  will 
leave  a  path  strewn  with  the  wreckage  of  atoms,  all  broken  to 
pieces,  many  of  the  broken  parts  being  charged,  while  the  medium 
is  filled  with  the  disturbances  that  we  speak  of  as  radiations. 
In  order  to  describe  these  phenomena  we  may  consider  these 
changes  from  afar  and  under  conditions  of  comparative  rest  and 
quiet  or  we  may  bravely  try  to  establish  our  experimental  outfit 
on  the  rapidly  moving  alpha  particle  itself.  And  the  results 
of  the  two  methods  of  observation  will  of  course  appear  very 
different  and  perhaps  for  a  long  time  we  will  be  unable  to  corre- 
late the  two  sets  of  observations. 

The  charge  of  the  alpha  particle  will  cause  it  to  be  surrounded 
by  an  electric  field  which  will  be  comparatively  weak  if  the  field 
is  uniform.  If  however  our  place  of  observation  had  been  a  beta 
particle  moving  with  the  same  velocity  the  potential  of  the  par- 
ticle would  be  a  million  volts  and  we  would  have  been  forced  to 
develop  a  laboratory  and  a  system  of  science  that  would  apply 
to  these  conditions  of  intense  electric  fields. 

Let  us  now  try  to  measure  time  on  the  alpha  particle.  In  the 
first  place  we  have  never  devised  a  clock  except  for  conditions  of 
comparative  rest.  Would  any  of  our  chronometers  run  regularly 
when  possessing  a  speed  of  120,000  miles  per  second?  If  the 
observer  was  6  ft.  from  the  clock  and  made  observations  by  sight 
the  clock  would  move  a  distance  of  4  ft.  while  the  light  was  pass- 
ing from  the  clock  to  the  observer,  assuming  that  the  velocity  of 


THE  GOAL  OF  THE  NEW  SCIENCE  3 

light  is  unaffected  by  the  velocity  of  the  observing  system. 
Would  not  the  measurement  of  time  greatly  depend  as  to  whether 
the  clock  and  the  observer  was  in  the  line  of  motion  of  the  alpha 
particle  or  not?  How  can  the  mass  of  a  body  be  determined  under 
these  conditions?  What  kind  of  observers  will  be  able  to  direct 
the  measurements?  Can  we  devise  an  automatic  set  of  appara- 
tus that  could  record  the  measurements  that  we  wish  to  have 
made  and  place  the  apparatus  on  the  alpha  particle?  These 
are  some  of  the  problems  that  confront  the  new  science  and  con- 
siderable advances  are  being  made  outlining  and  answering  some 
of  the  easier  of  these  problems. 

The  science  that  is  developed  on  the  rapidly  moving  alpha 
particle  may  then  be  called  the  alpha  particle  science.  As  the 
beta  particle  is  very  much  smaller  and  is  surrounded  by  a  very 
intense  electric  field  we  will  have  a  beta  particle  at  rest  physics 
and  a  rapidly  moving  beta  particle  physics.  Such  phenomena 
as  the  propagation  of  light  may  then  be  very  different  according 
as  we  view  them  from  our  own  standpoint,  in  regions  like  our 
own  but  with  very  intense  electric  fields,  or  from  rapidly  moving 
alpha  and  beta  particles.  The  new  science  aims  to  unify  all 
these  sciences  of  the  systems,  no  matter  how  differently  they 
may  appear,  into  one  harmonious  whole.  It  purposes  to  correlate 
the  laboratory  in  the  mind  with  the  laboratory  of  the  ishop. 
Length,  time,  and  the  other  "fundamental  units"  and  the  laws 
of  science  are  defined  and  measured  if  possible  under  every 
condition  that  is  known.  There  is  to  be  one  common  science 
based  on  the  same  laboratory  plan  for  the  inside  of  the  atoms, 
for  molecular  spaces,  for  conditions  as  they  may  exist  in  the  center 
of  the  sun  or  for  free  space. 

The  origin  of  the  new  science  is  to  be  found  in  the  new  geome- 
tries developed  from  axioms  differing  from  those  assumed  by 
Euclid.  The  discovery  of  the  electron,  radioactivity,  and 
studies  in  radiation  and  the  propagation  of  light  with  reference 
to  the  earth's  motion  have  furnished  the  beginnings  and  the 
outlook  of  the  new  fields  to  be  covered.  On  account  of  the 
prominent  role  played  by  electrical  phenomena  it  is  necessary 
to  restrict  this  treatment  largely  to  a  decription  of  an  ensemble 
of  electrical  charge,  mass  and  energy,  for  so  far  as  we  know 
electrical  charge  always  appears  with  a  certain  quantity  of 
mass  and  energy,  the  latter  being  usually  of  the  potential  type. 
As  all  knowledge  comes  to  us  through  the  senses,  it  seems  well 


4  FUNDAMENTAL  PHYSICS 

to  consider  very  briefly  the  transformations  in  phenomena 
imposed  upon  us  by  the  gateways  of  the  senses  and  to  indicate 
how  it  may  be  possible  to  introduce  laboratory  methods  into 
mental  phenomena.  The  various  entity  systems  are  viewed 
in  regard  to  the  problems  introduced  for  the  new  science  and  an 
outline  is  given  of  a  possible  system  of  laboratory  method  that 
would  be  applicable  to  all  of  these  entity  systems. 

All  of  our  scientific  advances  by  the  laboratory  method  have 
shown  that  the  magnitudes  of  quantities  defined  by  the  expres- 
sions "greater  than"  or  "less  than"  are  constituted  of  parts. 
These  parts  have  been  sorted  into  classes,  the  parts  in  each  class 
being  found  to  be  alike  in  some  or  all  of  their  properties.  The 
smallest  parts  of  a  magnitude  will  be  called  the  elements  or 
atoms  of  that  magnitude.  The  citizens  of  a  nation  constitute 
its  elements  or  the  atoms  of  ordinary  masses  of  matter,  its 
elements.  The  term  element  as  thus  used  depends  upon  the 
point  of  view  and  is  a  relative  term.  The  term  ultimate  element 
could  be  defined  as  the  smallest  magnitude  that  any  quantity 
can  be  partitioned  into.  Thus  as  far  as  we  -know  the  electron 
is  the  ultimate  element  of  electrical  charge  and  it  may  be  one 
of  the  ultimate  elements  of  the  universe  in  the  absolute  sense 
if  the  electron  does  not  possess  parts  or  as  we  may  say  a 
"structure."  In  the  vortex  ether  theory  of  matter  there  was 
only  one  ultimate  element  of  the  universe  as  regards  ordinary 
matter  and  free  space. 

A  natural  system  such  as  a  star,  an  animal,  a  magnet  or  an 
electron  will  be  spoken  of  as  an  entity  or  an  entity  system.  A 
laboratory  or  an  assumed  grouping  of  elements,  such  as  a  cavity 
of  radiations  used  in  the  definition  of  a  black  body  will  be  called 
an  ensemble.  An  aim  of  science  is  to  discover  the  ultimate 
elements  and  to  explore  and  derive  laws  for  the  simplest  en- 
sembles. As  an  example  of  this  kind  of  problem  we  might 
consider  space  or  the  free  ether  as  we  will  name  it.  In  many 
theories  the  free  ether  is  assumed  to  be  isotropic  and  to  be  without 
structure.  How  can  it  be  possible  to  apply  the  term  extension 
to  such  an  ether  for  there  is  no  way  of  defining  direction?  How 
is  there  to  be  any  relation  tp  time  for  in  any  such  ether  it  would 
be  impossible  to  measure  time.  Terms  such  as  time  and  direc- 
tion are  therefore  meaningless  for  such  an  ether  because  there 
is  no  way  to  define  them.  There  is  then  no  time  or  direction 
qualities  to  an  isotropic  ether  possessing  no  structure. 


THE  GOAL  OF  THE  NEW  SCIENCE  5 

Consider  an  ensemble  of  the  above  ether  and  radiation  ele- 
ments. If  this  ensemble  is  without  a  structure  how  can  we  define 
a  length  because  we  must  possess  some  marking  elements  for 
a  unit  of  length  or  how  can  we  speak  of  time  in  such  an  ensemble 
because  we  are  unable  to  measure  length?  For  the  above  en- 
semble the  velocity  of  the  radiation  cannot  be  employed  to  meas- 
ure time  because  there  is  no  way  of  defining  length.  For  this 
ensemble  of  ether  and  radiation  the  terms  length,  direction 
and  local  time  can  possess  no  local  meaning  but  must  be  received 
from  some  other  ensemble.  For  a  medium  as  the  ether  to  be 
intelligible,  to  possess  directed  qualities  and  to  be  described 
by  equations,  employing  terms  such  as  length  and  time,  it  is 
necessary  that  it  possess  a  structure  and  certain  other 
"  fundamental "  qualities. 

The  new  science  develops  a  consistent  and  a  local  philosophy 
for  each  ensemble  and  determines  as  fundamental  a  system  of 
local  definitions,  units  and  laws  as  possible.  The  laws  of  the 
transformations  of  the  local  philosophies  of  the  different 
ensembles  is  then  determined.  The  philosophy  that  possesses 
the  most  universal  application  a,mong  the  natural  entities  and 
whose  convenience  is  greatest  may  then  be  adopted  for  general 
use. 


5.  THE  DISAPPEARANCE  AND  CONSERVATION  OF 
ENERGY,  ELECTRICAL  CHARGE  AND  MASS 

It  has  long  been  assumed  that  energy  disappears  or  changes 
its  form  and  one  can  consider  phenomena  as  largely  if  not 
altogether  marked  by  energy  changes.  To  us  the  conception 
of  energy  is  most  satisfying  when  we  consider  kinetic  energy 
or  one-half  mv2.  Potential  energy  is  in  an  intangible  condition 
or  form  for  how  can  we  conceive  of  this  energy  as  existing  except 
in  the  medium  or  the  ether.  Since  we  apparently  know  so  little 
of  the  ether  we  can  almost  speak  of  the  energy  as  being  lost. 
The  classical  illustration  of  the  transformations  of  kinetic  and 
potential  energy  is  that  of  the  vibrating  pendulum.  In  the 
middle  of  its  swing  the  energy  is  all  kinetic  while  at  the  ends  of 
the  swing  the  energy  is  all  potential.  Our  laboratory  work  con- 
sists of  experiments  with  the  energy  in  the  kinetic  form.  To  be 
studied  energy  must  first  be  converted  into  the  kinetic  form 
adapted  to  the  problem  at  hand.  A  piece  of  uranium  or  a  piece 
of  coal  can  be  used  as  regards  their  radioactive  or  chemical  energy 
content  only  when  radioactive  energy  or  when  heat  is  developed. 

The  law  of  the  conservation  of  energy  is  found  to  hold  when 
we  consider  the  existence  of  the  two  forms  of  energy  and  we  feel 
entirely  justified  in  treating  potential  energy  as  "existing" 
in  the  same  way  as  kinetic  energy  because  it  can  be  converted 
into  the  kinetic  form. 

Our  ordinary  world  as  we  see  it  every  day  is  one  in  which 
kinetic  energy  is  usually  being  converted  back  and  forth  into 
potential  or  "heat"  energy.  And  it  requires  much  of  our  engi- 
neering effort  to  maintain  our  kinetic  condition.  Friction  is  ever 
working  against  the  moving  elements.  Most  of  us  are  kept 
busy  to  keep  things  going.  Even  in  the  astronomical  world 
the  philosophy  of  many  is  that  the  suns  are  becoming  cold  and 
dead  and  that  the  revolving  planets  and  moons  are  slowing  down 
in  their  motion.  Yet  this  death  of  kinetic  energy  that  is  every- 
where about  us  and  which  we  will  designate  as  a  condition  of 
our  type  of  physical  world  is  counteracted  by  more  or  less 
unknown  elements  so  that  conservation  may  always  apply. 


THE  DISAPPEARANCE  OF  ENERGY  7 

The  energy  world  is  then  ruled  by  these  conditions:  energy  is 
conserved:  the  energy  changes  of  our  every  day  life  is  marked 
by  the  natural  tendency  of  kinetic  energy  to  disappear:  and  the 
second  law  of  thermodynamics  which  may  be  stated  in  a  number 
of  forms  such  as  the  ever  increasing  value  of  the  entropy  content 
of  any  isolated  system,  the  impossibility  of  perpetual  motion 
apparatus  or  the  ever  tendency  of  the  universe  to  run  down 
as  regards  many  energy  changes  (in  the  same  way  as  a  clock,  the 
potential  energy  of  the  spring  being  converted  into  the  kinetic 
energy  of  the  pendulum  and  this  kinetic  energy  changed  gradually 
into  the  kinetic  energy  of  heat  motions). 

The  continual  flow  of  energy  through  so  many  transforma- 
tions leads  one  to  suppose  that  when  it  ultimately  is  found  to 
consist  of  units,  particles,  quanta,  entities,  atoms  or  whatever 
term  we  may  call  them,  these  ultimate  elements  may  be  all  alike 
because  all  quantities  of  energy,  like  electrical  charges,  depend 
upon  the  total  amount  of  energy  present  and  are  independent 
of  the  nature  of  the  elements  of  energy  combined  to  form  the 
whole. 

The  appearance  of  electrical  charges  bears  some  analogies 
to  the  appearance  of  energy.  The  commercial  problems  relating 
to  electricity  have  to  do  with  the  generation,  the  transmission 
and  the  absorption  of  charges  of  electricity,  the  phenomena  of 
magnetism  being  assumed  as  being  due  to  the  motion  of  electrical 
charges.  The  constitution  of  electrical  charges  is  very  simple 
in  that  all  electrical  charges  appear  to  be  built  of  elementary 
parts  all  having  the  magnitude  of  4.7  (10)~10  e.s.  units,  all  these 
units  being  identical  except  as  they  may  be  positive  or  negative 
in  character. 

Like  kinetic  energy  electrical  charges  never  appear  except  in 
connection  with  masses  of  matter  thus  making  the  trio  of  kinetic 
energy,  mass  and  electrical  charge  an  inseparable  ensemble  as 
far  as  experimental  knowledge  extends.  As  kinetic  energy  is 
characterized  by  its  tendency  to  disappear  so  free  electrical 
charges  always  disappear  unless  special  precautions  are  taken  to 
prevent  this  change.  The  electrical  elements  possess  the  unique 
property  however  of  neutralizing  themselves  in  that  the  approach 
of  equal  charges  of  positive  and  negative  electrical  discharges 
causes  the  more  or  less  complete  disappearance  of  the  charges. 

The  smallest  element  of  negative  electricity,  the  electron, 
is  associated  with  a  mass  of  matter  about  the  one-eighteen 


8  FUNDAMENTAL  PHYSICS 

hundredth  part  of  that  of  the  smallest  element  of  matter,  the 
hydrogen  atom.  Since  the  ratio  of  mass  to  charge  is  found  to 
vary  with  the  velocity  of  the  electron  it  has  been  assumed  that 
this  mass  is  variable  rather  than  the  electrical  charge.  Experi- 
mentally the  magnitude  that  is  measured  is  the  ratio  of  the 
charge  to  the  mass  so  that  for  the  rapidly  moving  electron  we 
have  a  condition  arising  where  electrical  charge,  mass  and  of 
course  the  kinetic  energy  appears  as  a  variable  ensemble  for 
which  no  experiment  has  been  devised  that  will  permit  of  the 
determination  of  the  varying  elements. 

As  the  philosophy  that  assumes  that  natural  phenomena 
are  extremely  simple  has  led  to  many  of  the  greatest  discoveries, 
so  the  assumption  that  the  magnitude  of  the  electrical  charge 
is  constant  rather  than  the  mass  of  the  electron,  makes  the  treat- 
ment of  the  ensemble  of  energy,  charge  and  mass  more  simple 
and  apparently  just  as  accurate  as  would  any  other  assumption. 
The  law  of  the  conservation  of  electrical  charge  can  thus  be 
considered  to  be  absolute.  The  second  law  and  the  general 
condition  that  applies  to  electrical  charges  is  that  all  the  natural 
changes  in  a  closed  electrical  system  are  such  as  to  make  the 
magnitude  of  the  free  charge  a  minimum. 

No  positive  electrical  charge  has  been  found  except  as  being 
associated  with  atoms  of  matter  and  the  view  commonly  held  is 
that  the  positive  charges  are  an  essential  part  of  the  nuclei  of  the 
atoms.  The  generation  of  free  charges  of  electricity  always 
results  in  the  disappearance  of  energy.  The  disappearance  of  free 
electrical  charges  always  takes  place  in  matter  and  the  picture  of 
the  process  assumes  that  the  positive  and  negative  charges 
neutralize  each  other  inside  the  molecules  and  atoms.  The  energy 
that  is  lost  in  the  generation  of  free  charges  is  considered  as  the 
energy  of  the  electrical  field  between  the  positive  and  negative 
charges  and  that  on  the  localization  of  the  electrical  field  inside 
of  atoms  or  molecules  some  of  its  potential  energy  is  changed  into 
kinetic  energy. 

As  in  energy  changes  the  disappearance  of  kinetic  energy  was 
considered  as  accompanied  by  the  appearance  of  an  equal  amount 
of  potential  energy  in  the  ether  so  the  disappearance  of  negative 
charges  into  molecules  and  atoms  could  be  associated  with  the 
appearance  of  certain  characteristics  of  matter  which  we  ordi- 
narily associate  with  the  neutral  state.  In  other  words  the  char- 
acteristic properties  of  matter  may  be  those  associated  with  what 


THE  DISAPPEARANCE  OF  ENERGY  9 

we  consider  as  matter  after  it  has  lost  all  of  its  electrons.  Such 
matter  we  will  speak  of  as  "natural"  or  "free"  matter.  "Ordi- 
nary" matter  will  be  called  "neutral"  matter.  All  electrical 
charges  then  become  aggregates  of  electrons  and  all  masses 
become  aggregates  of  electrons  and  the  "atoms'7  of  "natural" 
matter. 

The  constitution  of  matter  is  found  to  be  atomic,  all  matter 
being  built  out  of  some  92~elementary  atoms  with  accumulating 
evidence  that  these  atoms  may  themselves  be  composed  of  much 
simpler  systems  such  as  hydrogen  or  helium.  The  fundamental 
property  of  matter  is  usually  believed  to  be  its  mass  and  the 
science  of  chemistry  is  based  on  the  assumption  that  mass  is 
conserved.  We  have  seen  that  the  mass  of  the  electron  is  con- 
sidered as  a  variable.  Whether  this  kind  of  mass  is  acted  upon 
by  gravitational  forces  remains  for  future  experiments  to  deter- 
mine and  whether  the  mass  of  the  various  atoms  varies  as  does 
that  of  the  electron  at  high  speeds  also  remains  for  future  investi- 
gations to  tell.  There  may  be  an  electrical  and  a  material  mass, 
or  a  kinetic  and  a  potential  mass  corresponding  to  the  energy 
terms.  The  law  of  .conservation  might  be  considered  as  apply- 
ing to  the  two  types  of  mass.  "Natural"  matter  would  always 
naturally  disappear  into  ordinary  or  neutral  matter  and  the  law 
corresponding  to  the  second  law  of  thermodynamics  would  be  that 
the  complex  atomic  systems  are  running  down  or  in  other  words 
the  radioactivity  of  the  elementary  atoms  always  results  in  simpler 
atomic  systems  through  the  disintegration  of  the  more  complex 
atoms. 

The  law  of  conservation  and  the  disappearance  of  kinetic 
energy,  electric  charge  and  natural  matter  appear  to  be  the  same. 
These  elements  naturally  partition  themselves  between  the  ether 
and  neutral  matter.  Neutral  matter  is  then  the  vehicle  of  ki- 
netic energy,  electrical  charge  and  natural  matter.  The  disappear-, 
ance  of  kinetic  energy,  of  free  electric  charges  or  of  natural  matter 
is  accompanied  by  potential  energy  changes  for  which  the  ether  is 
the  vehicle.  The  ether  about  an  ensemble  of  energy,  charge  and 
natural  matter  may  be  considered  to  be  in  a  state  or  to  be 
approaching  a  state  of  equilibrium  with  the  ensemble.  Thus  the 
ether  about  ordinary' matter  could  be  considered  as  "ordinary" 
ether  and  might  be  the  same  or  different  from  the  ether  at  a  very 
great  distance  from  any  of  these  elements  or  from  ensembles  of 
one  or  more  of  these  elements.  Experimental  work  of  the  most 


10  FUNDAMENTAL  PHYSICS 

fundamental  character  remains  to  be  done  as  to  the  relations 
between  the  free  ether,  energy,  electric  charge,  and  natural  matter 
and  the  partitioning  of  these  elements  between  ordinary  ether 
and  matter.  The  law  of  conservation  applies  by  definition  to 
electrical  charges  absolutely  and  to  energy  and  mass  only  as  ele- 
ments in  a  closed  ensemble  of  ether,  energy,  matter  and  charge. 

The  writer  proposes  the  ether  to  be  an  analogue  of  matter 
possessing  a  much  more  fine  grained  structure.  The  elements  of 
electrons  and  natural  atoms  of  matter  become  the  electroethons 
of  the  ether.  The  potential  or  hidden  energy  becomes  the  kinetic 
energy  of  the  electroethons.  The  vibrations  and  sound  waves  of 
neutral  matter  are  paralleled  by  the  electromagnetic  waves  of  the 
ether.  As  sound  waves  are  pictured  as  the  ordered  collisions  of 
particles  of  matter  so  the  electromagnetic  waves  are  the  ordered 
collisions  of  electroethon  particles.  For  purposes  of  illustra- 
tion rather  than  as  an  exact  analogue  there  can  be  pictured  an 
atmosphere  of  mobile  electroethons  in  a  lattice  work  of  immobile 
electroethons  somewhat  similar  to  the  existence  of  an  atmosphere 
of  electrons  in  a  framework  of  the  natural  atoms  of  matter  in  a 
metal.  An  electric  field  is  a  region  of  the  ether  where  the  neutral 
condition  has  been  disturbed  in  much  the  same  way  that  an 
electromotive  force  disturbs  the  condition  of  equilibrium  of 
the  electron  atmosphere  of  a  metal. 

In  treating  the  second  law  of  thermodynamics  Maxwell  con- 
sidered that  there  could  be  "demons"  that  could  reverse  the 
changes  whose  direction  was  given  by  the  law.  Our  credo  as 
optimists  leads  us  to  believe  that  there  are  "angels"  that  can 
direct  the  transformation  of  any  natural  phenomena.  For 
example  the  direction  of  the  radioactivity  of  matter  is  that  of  the 
disintegration  of -the  more  complex  elements.  We  believe  that 
experimental  discoveries  will  be  made  that  will  indicate  how 
"angels"  (and  perhaps  ourselves)  can  build  the  more  complex 
atoms  from  the  simpler  conserved  elements.  These  "angels" 
might  possibly  work  in  the  center  of  the  sun,  in  very  intense  elec- 
tric fields  or  by  "breaking  down"  the  ether  under  electrical 
stresses  so  that  even  electrical  charges  or  natural  atoms  would 
result.  And  the  Director  of  these  "angels"  we  might  define  as 
the  "Creator"  or  "Ruler"  of  the  Universe,' and  this  form  of  phi- 
losophy as  "monotheism." 

As  regards  kinetic  energy  we  know  that  its  magnitude  is 
relative  depending  on  how  %mv2  is  defined  and  measured. 


THE  DISAPPEARANCE  OF  ENERGY  11 

Presumably  potential  energy  and  possibly  mass  and  electrical 
charge  may  be  viewed  in  the  same  way  for  the  latter  two  quan- 
tities are  measured  by  "forces"  and  accordingly  if  the  system 
upon  which  measurements  were  being  made  was  subjected  to 
acceleration  the  measurements  would  be  subject  to  modification. 
The  condition  of  relativity  thus  appears  amongst  the  conserved 
elements.  An  example  of  such  relativity  is  that  of  electrical 
charge  and  mass.  No  electrical  charge  has  ever  been  separated 
entirely  from  a  mass,  the  electron  possessing  a  certain  charge 
and  a  certain  mass  defined  with  reference  to  the  system  with 
reference  to  which  its  motion  is  measured. 

These  problems  as  to  the  way  the  ether  is  modified  by  its 
energy  content  are  very  important  and  can  be  studied  by  the 
effect  produced  upon  the  velocity  of  the  electromagnetic  ra- 
diations (the  writer  is  now  engaged  in  experiments  of  this  kind) . 
Indeed  apparently  no  more  fundamental  and  isolated  experiments 
can  be  performed  because  these  are  the  simplest  ensembles  at 
present  open  to  the  new  science. 

The  marked  effects  of  electric  charges  and  natural  matter 
upon  the  ether  (the  electric  and  magnetic  fields),  the  apparent 
absolute  conservation  of  these  elements  and  their  disappearance 
by  their  "mutual  neutralization"  have  few  analogues  in  the 
coarser  grained  entity  systems  unless  we  consider  phenomena  like 
the  formation  of  salts  from  acids  and  bases,  the  phenomena  of 
permanent  magnetism  and  some  life  phenomena. 

Experiments  have  already  indicated  that  the  structure  of 
electrical  charge  is  more  "fine  grained"  than  that  of  ordinary 
neutral  matter  though  the  atoms  of  natural  matter,  the  positive 
nuclei  of  the  ordinary  atoms,  possess  about  the  same  size  as  the 
electron.  The  "fineness"  of  structure  of  natural  matter  is  thus 
made  to  depend  upon  the  magnitude  of  the  nuclei  of  the  atoms. 
The  ultimate  and  individual  elementary  units  of  energy  and  of 
the  ether  have  not  been  discovered  experimentally  and  it  is 
reasonable  to  assume  that  these  elements  are  much  finer  grained 
than  mass  or  electrical  charge. 

From  the  Zeeman,  Stark  and  similar  effects  and  the  modifi- 
cation of  the  velocity  of  electromagnetic  radiations  by  matter  it 
seems  certain  that  electrical  charges  remain  as  such  in  the  neutral 
atomic  and  molecular  systems.  The  disappearance  of  energy 
and  mass  in  the  ether  without  changing  its  properties  to  any  great 
extent  would  lead  us  to  believe  that  the  ether  may  be  such  a 


12  FUNDAMENTAL  PHYSICS 

"dense"  energy  and  mas§  medium  that  the  increment  due  to 
these  disappeared  elements  affects  the  "density"  but  little.  The 
older  elastic  ether  theory  developed  from  these  disappearance 
phenomena. 

The  possible  conditions  of  relativity  in  any  ensemble  are  so 
numerous  that  it  is  always  highly  important  to  reduce  the  num- 
ber of  elementary  units  in  the  ensemble  to  the  minimum.  The 
new  science  aims  to  obtain  the  ultimate  units  or  atoms  of  all  the 
entity  systems  of  the  universe  and  then  consider  if  any  of  the 
properties  of  these  elementary  atoms  can  be  defined  as  "ab- 
solute" in  the  sense  of  "nondisappearing."  Other  elements 
will  then  be  described  relative  to  the  "absolute"  elements.  If 
the  elements  that  appear  to  be  definable  in  an  "absolute"  man- 
ner do  not  determine  a  physics  uniquely  then  the  new  science 
will  develop  all  the  consistent  systems  of  physics  that  appear  to 
equally  simulate  phenomena  and  employ  the  system  that  is 
simplest  and  most  convenient. 


6.  IONIZATION  PHENOMENA 

According  to  the  freedom  of  neutral  atoms  of  matter  we  clas- 
sify bodies  into  solids,  liquids  and  gases.  In  solids  the  atoms  may 
possess  an  orderly  arrangement  in  planes  (as  is  the  case  in  crys- 
tals) or  a  more  or  less  disordered  arrangement  (as  in  substances 
such  as  glass).  The  atoms  are  not  free  to  move  about.  In 
liquids  the  molecules  possess  some  freedom  of  movement  but  are 
not  "free."  In  gases  the  molecules  are  comparatively  "free" 
except  during  collisions.  The  kinetic  energy  content  increases  as 
one  passes  from  solid  to  liquid  to  gas. 

Electrical  charges  are  "bound"  in  neutral  matter.  The 
"binding"  is  greatest  in  the  insulators  or  nonconductors.  It 
becomes  very  much  less  in  electrolytes  when  a  difference  of  po- 
tential of  a  few  volts  will  "free"  the  charges.  It  is  least  in  metals 
where  an  "electron  atmosphere"  or  electron  gas  is  quite  "free" 
to  be  acted  upon  by  very  small  electromotive  forces. 

Temperature  can  be  employed  as  a  measure  of  the  kinetic 
energy  of  molecules  when  in  the  gaseous  state.  The  absolute 
zero  of  temperature  being  a  condition  where  the  kinetic  energy 
vanishes.  Conductivity  varies  as  the  freedom  of  the  electrical 
charges  in  matter  and  .becomes  practically  perfect  for  metals  for 
the  absolute  zero  of  temperature.  Electrical  currents  will  flow 
in  metals  at  very  low  temperatures  for  hours  after  the  applied 
e.m.f.  has  been  discontinued. 

High  temperatures  of  all  substances  results  in  their  intense 
ionization  and  increased  conductivity.  The  upper  limit  of 
temperature  results  from  the  generation  of  free  electrical  charges 
or  ions  and  the  flow  of  kinetic  energy  into  "potential  energy" 
then  restricts  the  attainment  of  any  highei^temperatures.  The 
density  of  the  potential  energy  may  be  assumed  to  measure  the 
"temperature"  of  the  electroethons. 

The  motion  of  atoms  or  molecules  in  solids  and  of  ions  in  non- 
conductors is  ordered  and  consists  largely  of  oscillations  about 
positions  of  equilibrium.  The  motion  of  molecules  and  ions  in 
liquids  is  more  disordered.  The  motion  of  molecules  in  gases,  of 
electrons  in  metals  and  of  ions  in  substances  at  high  temperatures 

13 


14  FUNDAMENTAL  PHYSICS 

is  largely  disordered,  the  values  of  the  "free  paths"  and  velocities 
of  the  particles  following  Maxwell's  law  and  being  that  of  the 
variation  in  the  distance  of  the  bullet  marks  on  a  bull's  eye  pat- 
tern used  as  a  target  in  rifle  practice. 

Ordered  motions  are  added  to  the  natural  motions  when  a 
direct  electric  current  flows  through  a  metal,  a  vacuum  tube  or 
any  conducting  substance,  when  heat  flows,  or  when  a  mechan- 
ical pressure  is  transmitted.  Alternating  motions  are  added  to 
the  natural  motions  when  alternating  currents  of  electricity,  heat, 
or  mechanical  pressure  or  sound  waves  are  transmitted  through  a 
substance. 

Thanks  to  the  existence  of  electron  atmospheres  we  are  able  to 
cover  the  earth  with  a  network  of  cables,  telegraph,  telephone  and 
electric  power  transmission  lines.  We  can  picture  these  as 
"electric  lines  of  force"  making  a  loose  lattice  work  everywhere. 
The  electric  cars  would  be  the  "ions"  following  the  "electric 
lines  of  force  of  the  polarized  electric  field" — the  cables  overhead 
or  beneath  the  electric  car.  The  atoms  and  molecules  could  be 
represented  by  the  trains  on  the  railroads  and  the  automobile 
trucks  on  the  national  highways.  The  locomotives  are  the 
"energized"  atoms  giving  kinetic  energy  to  the  train  molecules. 
The  chunks  of  coal  and  the  tanks  of  gasoline  are  the  quanta, 
radions  or  elements  of  radiation  that  are  being  partitioned  to  the 
molecular  elements.  Coal  and  gasoline  represent  "potential," 
stored  or  lost  kinetic  energy.  The  motion  of  the  automobile 
trucks  is  disordered  and  is  represented  by  gas  motions  while  the 
motive  electric  cars  in  a  city  are  more  like  the  motions  taking 
place  in  the  lattice  work  of  solids  and  liquids. 

The  analogy  between  our  system  of  electrical  current  trans- 
mission by  threads  of  electron  atmospheres  and  the  lattice  line 
structure  of  an  atmosphere  of  electroethons  indicates  that  the 
supposed  difficulty  of  the  ether  problems  may  not  be  as  great  as 
at  first  surmised.  In  the  first  place  we  at  first  feel  that  a  system 
of  matter  could  with  difficulty  pass  through  an  ether  lattice  work. 
The  diameter  of  an  atom  is  about  10~8  cm.  while  the  diameters 
of  the  atom  nucleus  and  the  electron  are  about  10~13  cm.  The 
emptiness  of  the  atom  is  then  equivalent  to  the  emptiness  of  the 
United  States  when  filled  with  about  1000  buildings  30  ft.  square. 
Even  though  a  large  part  of  our  population  enjoy  the  telephone 
and  the  electric  current  the  "porosity"  of  these  electron  atmos- 
pheric threads  through  the  country  is  "extremely  tenuous." 


IONIZATION  PHENOMENA  15 

Each  atom  could  be  cut  by  an  ether  thread  and  yet  the  ether  lat- 
tice structure  could  be  much  more  tenuous  than  our  lattice  sys- 
tem of  telephone  threads.  The  nature  of  the  ions  and  the 
ionic  radiations  will  permit  an  outline  the  electron  and  "natural 
matter"  world. 

An  ion  consists  of  a  certain  amount  of  electrical  charge  with  a 
certain  quantity  of  matter.  Experimental  evidence  indicates 
that  every  atom  of  matter  contains  one  or  more  atoms  of  negative 
electricity  or  electrons.  These  electrons  may  be  ejected  from 
the  atoms  or  molecules  of  matter  under  certain  conditions,  leav- 
ing the  atoms  or  molecules  positively  charged.  The  atoms  or 
molecules  may  gain  or  lose  negative  electrons  and  by  this  means 
an  innumerable  number  of  different  kinds  of  negative  and  posi- 
tive ions  can  be  formed.  All  kinds  of  ions  are  combinations  of 
atoms  and  molecules  that  have  either  lost  or  gained  electrons. 

Ions  composed  of  a  comparatively  small  number  of  atoms  or 
molecules  are  called  simple  ions.  Thus  the  ions  produced  in 
chemically  pure  gases  at  low  pressures  are  simple  ions.  When 
the  gases  are  not  pure;  when  fog,  dust  and  similar  particles  are 
present,  the  ions  may  be  very  complex.  The  ions  resulting  from 
many  kinds  of  chemical  reactions  such  as  those  to  be  found  in 
the  neighborhood  of  flames  are  complex.  There  is  probably 
no  sharp  dividing  line  in  the  above  classification,  the  division 
being  one  of  convenience. 

An  ion  is  a  charged  particle  that  may  be  considered  to  be 
practically  at  rest  or  at  least  it  does  not  possess  any  greater  kine- 
tic energy  than  does  a  gaseous  molecule  at  the  same  temperature. 
It  may  be  given  kinetic  energy  of  motion  by  the  action  of  an  elec- 
tric field.  The  "particles"  that  constitute  radiations  such  as 
a,  /3  or  cathode  ray  particles  are  moving  rapidly  and  are  not 
usually  spoken  of  as  ions. 

Under  no  condition  is  the  number  of  free  ions  in  a  given  space 
of  the  same  order  of  magnitude  as  the  number  of  atoms.  Ionizing 
agents  in  general  produce  equal  numbers  of  positive  and  negative 
ions  or  at  least  this  is  usually  assumed  to  be  the  case.  It  is 
possible  that  the  ions  formed  may  possess  charges  of  different 
magnitude  so  that  the  number  of  positive  ions  need  not  neces- 
sarily be  equal  to  the  number  of  negative  ions.  It  requires 
some  time  for  an  ionizing  agent  to  act  before  the  number  of 
ions  being  formed  is  equal  to  the  number  of  positive  and  negative 
ions  recombining.  It  is  in  phenomena  of  this  kind  that  the 


16  FUNDAMENTAL  PHYSICS 

term  coefficient  of  recombination  is  used.  This  coefficient  is 
probably  not  a  constant  but  depends  upon  the  process  under 
which  ionization  takes  place.  In  most  cases  the  production 
of  ions  is  approximately  uniform  throughout  any  given  body 
and  under  these  conditions  the  coefficient  is  practically  a  con- 
stant. The  term  coefficient  of  diffusion  is  defined  in  the  same 
way  as  in  the  theory  of  gases.  Its  constancy  also  depends  upon 
the  uniformity  of  the  ionization. 

Any  gas  that  is  ionized  when  placed  between  electrodes 
maintained  at  a  certain  difference  of  electrical  potential  will 
permit  an  electrical  or  ionization  current  to  flow.  This  current 
increases  to  a  maximum  value  called  the  saturation  current 
for  an  increase  in  the  potential  difference  up  to  a  certain  value 
called  the  saturation  potential  difference.  These  current  poten- 
tial curves  depend  upon  the  nature,  the  pressure,  the  tem- 
perature, etc.,  of  the  ionized  medium.  They  also  depend  upon 
the  nature  of  the  ionizing  agent. 

In  ionization  literature  the  terms  ray  and  radiation  are  often 
used  indiscriminately.  x-"rays"  and  x  "radiations"  are  both 
used.  The  term  "ray"  applies  to  the  emission  from  "z-ray" 
tubes  and  from  the  radioactive  bodies.  Thus  we  have  a,  /3, 
7,  5  and  x-rays,  recoil  rays,  cathode  and  the  various  vacuum 
tube  rays.  When  the  nature  of  the  emitted  particle  or  wave 
is  characteristic  and  possesses  properties  that  can  be  accurately 
measured,  the  term  radiation  is  used.  Thus  we  have  black 
body  radiations,  the  radiations  from  definite  radioactive  prod- 
ucts, characteristic  x  radiations,  etc.  The  term  secondary 
radiation  is  generally  used  because  these  radiations  are  often 
characteristic  of  the  kind  of  matter  emitting  them.  The  terms 
"ray,"  "beam  of  rays,"  "pencil"  of  rays,  etc.,  are  used  in  much 
the  same  way  as  they  are  used  in  optics. 

It  may  be  considered  convenient  to  classify  radiations  into 
the  "bullet"  or  atomistic  and  the  "medium"  types.  7  and 
x-rays  are  of  the  wave  or  pulse  type.  Experimental  evidence 
indicates  that  the  ionization  produced  by  the  x  and  7  rays  is 
due  to  the  secondary  radiations  excited  by  these  rays.  Indeed 
it  may  be  possible  that  all  ionizing  rays  consist  of  moving 
particles,  these  particles  being  invariably  charged.  According 
to  this  view  the  process  of  ionization  would  be  a  collision  phe- 
nomena, the  resultant  ions  being  due  to  the  action  of  an  electric 
field  upon  molecules  or  atoms. 


IONIZATION  PHENOMENA 


17 


Primary  Radiations 
I.  Electromagnetic  radiations: 

1.  Hertzian  waves. 

2.  Reststrahlen  and  radiant  heat. 


3.  Light... 


4.  Ultraviolet  light. 


5.  X-rays. 


II.  Cathode  rays 


III.  Ionic  radiations  due  to  the  action 
of  the  electric  force: 


1.  Anode  or  positive  rays 


2.  Canal  rays. 

3.  Negative  rays. 

4.  Entladungstrahlen. 

5.  Magnetic  rays. 

6.  Neutral  rays.   "Retrograde" 
rays    are    probably    neutral 
during  a  large  portion  of  their 
path. 

IV.  Thermionic  radiations: 

1.  Electron  radiations. 

2.  Rays  of  positive  and  negative 
ions  and  neutral  matter. 

2 


Secondary  Radiations 


(a)  Normal  photo-electron  radia- 
tions. 

(6)  Selective  photo-electron  radia- 
tions. 

(a)  Normal  photo-electron  radia- 
tions. 

(6)  Selective  photo-electron  radi- 
tions. 

(c)  Secondary  cathode  rays. 

(a)  Secondary  cathode  rays. 

(6)  5  rays. 

(c)  Secondary  scattered  x-rays. 

(d)  Homogenous  x  radiations. 
(a)  Secondary  cathode  rays. 
(6)  Secondary  x-rays. 

(i)  Homogenous  x  radiations 
characteristic  of  the  anti- 
cathode. 

(ii)  Independent  x-rays  char- 
acteristic of  the  velocity  of 
the  primary  rays. 


(a)  Secondary  rays  produced  by 
neutral  rays.  These  may  con- 
sist of  positive  or  negative  ions 
or  of  neutral  particles. 

(6)  5  rays  or  slowly  moving 
electrons. 

(c)  Soft  x-rays  and  possibly  char- 
acteristic x  radiations  of  Sn 
and  Pb. 


18  FUNDAMENTAL  PHYSICS 


V.  Radioactive  radiations : 

1.  a  rays. 

Atoms  of  helium  with  a 
double  positive  charge. 

2.  ft  rays. 
Electrons. 


3.  y  rays. 


4-  Recoil  rays. 

Atoms  of  radioactive 
products. 


(a)  5  rays. 

(6)  Secondary  y  rays, 
(.c)  Secondary  recoil  rays, 
(a)  5  rays. 

(6)  Secondary  y  rays, 
(c)  Secondary  recoil  rays, 
(a)  Secondary  /3  rays. 
(6)  Secondary  scattered  y  rays, 
(c)  Homogenous  y  radiations, 
(a)  5  rays. 

(6)  Secondary  recoil  rays  consist- 
ing of  particles  struck  by  the 


primary  recoil  ray  particles. 
5.  Penetrating  radiation. 

Of  the  above  radiations,  photo-electron  radiations,  primary 
and  secondary  cathode  rays,  primary  and  secondary  ft  rays, 
high  temperature  negative  thermionic  radiations  and  5  rays 
consist  of  streams  of  rapidly  moving  electrons.  The  only  essen- 
tial difference  between  these  various  types  of  electron  radiation 
lies  in  the  fact  that  the  electrons  possess  different  velocities. 
5  rays  consist  of  very  slowly  moving  electrons.  ft  rays  derive 
their  energy  from  atoms  undergoing  radioactive  change  and  usu- 
ally consist  of  very  rapidly  moving  electrons.  Cathode  rays 
are  due  to  electrons  that  have  fallen  through  electric  fields  of  a 
certain  potential  difference  (7)  and  have  acquired  a  kinetic 
energy  %mvz  =  Ve. 

The  other  radiations  either  consist  of  "waves,"  "pulses," 
"entities"  or  moving  particles  composed  of  one  or  more  atoms  of 
matter,  a  rays  are  rapidly  moving  helium  ions  carrying  a 
double  positive  charge.  ft  and  7  rays  derive  their  energy  from 
atoms  undergoing  radioactive  change.  There  are  then  three 
types  of  high  speed  radiations,  the  ether,  electron  and  atomistic 
radiations.  All  these  radiations  are  ionizing  agents  except  the 
long  wave  length  ether  radiations. 

Ionizing  radiations  are  either  spontaneous  or  subject  to  ex- 
perimental control.  The  a,  ft  and  7  rays  are  spontaneous  in 
origin  and  their  initial  properties  on  emission  cannot  be  al- 
tered in  any  way  by  changes  in  the  surrounding  physical  and 
chemical  environment.  While  many  of  the  other  radiations 
are  emitted  by  atomic  or  molecular  systems,  these  systems  can 
be  controlled  in  certain  ways  by  the  action  of  outside  forces. 
Thermionic  radiations  depend  upon  the  temperature,  the  nature 


IONIZATION  PHENOMENA  19 

of  the  incandescent  surface,  etc.  The  nature  of  x-rays  depends 
upon  the  velocity  of  the  exciting  cathode  ray  particles. 

With  the  possible  exception  of  the  spontaneous  radiation,  all 
the  "material"  or  electron  radiations  are  due  either  to  the  exist- 
ence of  high  temperatures  or  to  electric  fields. 

Experimental  evidence  supports  the  view  that  only  material 
or  electron  radiations  produce  ionization  directly.  X  and  7 
rays  and  ultraviolet  light  seem  to  ionize  bodies  indirectly  through 
the  action  of  secondary  electron  radiations.  It  therefore  fol- 
lows that  the  ionization  of  neutral  particles  takes  place  during 
the  moments  of  collision  between  these  particles  and  the  rapidly 
moving  radiation  particles.  According  to  this  view  ionization 
is  a  collision  phenomenon. 

Though  intimately  related  in  the  phenomena  as  they  ac- 
tually take  place,  the  various  ionizing  radiations  can  be  discussed 
and  classified  according  to  the  changes  which  take  place  in  the 
radiations  when  they  pass  through  matter,  the  changes  pro- 
duced in  the  atoms  from  which  they  originate  and  the  changes 
produced  in  the  molecules  and  atoms  of  the  absorbing  matter.' 

(A)  Effects  on  the  ray  particles  and  beams  of  radiation  pro- 
duced by  the  atoms  and  molecules  of  absorbing  matter. 

(a)  The  ray  particles  lose  their  velocity.  This  decrease  of 
velocity  obeys  certain  laws  and  depends  upon  the  nature  of  the 
particles,  the  nature  of  the  atoms  with  which  they  come  into 
mutual  action  or  collision  and  the  dynamic  conditions  of  each 
collision.  (6)  The  rays  or  radiation  beams  lose  energy  due  to 
decrease  in  velocity  though  not  necessarily  according  to  the  or- 
dinary mechanical  relation,  (c)  The  ray  particles  or  entities 
may  disappear,  (d)  The  ray  particles  or  entities  may  be  trans- 
formed so  that  a  different  type  of  radiation  results,  (e)  The 
direction  of  the  rays  may  be  changed.  This  changed  part  may 
be  either  of  a  reflected  or  a  scattered  type. 

(B)  The  effects  that  take  place  during  the  formation  of  the 
radiation  particles  or  entities. 

(a)  The  velocity  of  a  and  0  particles  appears  to  be  related  to 
the  period  of  disintegration  of  the  parent  atom.  (6)  /?  and  7 
rays  are  usually  emitted  by  the  same  product  probably  simul- 
taneously, (c)  a  particles  may  be  emitted  in  pairs,  (d)  The 
emission  of  a  particles  often  precedes  the  existence  of  short  period 
disintegration  products,  (e)  The  parent  atom  may  become 
a  recoil  ray  particle.  (/)  The  emission  of  primary  rays  by  an 


20  FUNDAMENTAL  PHYSICS 

atom  may  be  accompanied  by  the  emission  of  secondary  radia- 
tion due  to  the  passage  of  the  primary  ray  particle  through  the 
atom,  (g)  Various  vibrations  and  changes  in  structure  of 
the  parent  atom  may  accompany  the  ejection  of  any  radiation 
particle  or  entity,  (ti)  The  energy  changes  due  to  the  forma- 
tion of  the  primary  and  secondary  radiation  particles  may  take 
place  according  to  the  elementarquanta  theory. 

(C)  Some  effects  produced  in  the  molecules  and  atoms  of 
the  matter  absorbing  the  given  radiation.  These  effects  may  be 
temporary  or  they  may  possess  any  degree  of  permanency. 

(a)  The  atoms  or  molecules  may  be  dissociated  into  neutral 
parts.  (6)  The  atoms  or  molecules  may  be  ionized.  The  ions 
may  be  formed  within  the  molecule  or  they  may  separate  from 
each  other  and  exist  as  independent  particles.  Secondary 
electrons  radiations  are  of  this  latter  type,  (c)  The  atoms, 
molecules  or  their  ions  may  be  caused  to  become  recoil  ray  par- 
ticles, (d)  Atoms  may  be  permanently  broken  down.  This 
constitutes  a  transmutation  of  the  element  and  has  not  been 
positively  proven  to  take  place,  (e)  The  atom  or  molecule  may 
be  caused  to  emit  some  of  its  intrinsic  energy.  This  constitutes 
a  "trigger"  effect  and  has  not  been  proven  to  take  place.  (/) 
The  atom  or  molecule  may  absorb  energy  and  store  it  in  a  ki- 
netic or  a  potential  form,  (g)  Parts  of  the  atom  or  molecule  may 
be  put  into  vibration.  This  may  result  in  a  transformation  and 
radiation  of  the  energy  absorbed.  Phosphorescence  and  fluores- 
cence are  examples  of  this  kind,  (h)  The  ionizing  particles 
may  combine  with  an  atom,  molecule  or  ion  and  form  a  new  sys- 
tem. The  resultant  particle  need  not  necessarily  be  a  radiation 
particle.  The  production  of  particles  by  dissociation,  ioniza- 
tion  and  possibly  by  transmutation  is  opening  a  new  field  in  dy- 
namical chemistry,  and  promises  much  from  both  the  theoretical 
and  practical  points  of  view. 

From  the  point  of  view  of  generating  the  ionizing  agents  many 
problems  arise.  Even  in  the  visible  part  of  the  spectrum  it  is 
very  difficult  to  obtain  monochromatic  light.  The  ordinary 
incandescent  lamp  does  not  possess  an  electric  current  to  light 
energy  emission  efficiency  of  more  than  a  few  (a)  per  cent,  and 
the  efficiency  of  converting  the  original  energy  of  the  coal  into 
electric  current  is  only  some  twenty  (6)  per  cent,  at  best. 

If  then  we  wish  to  generate  ultraviolet  light  of  X  2500  to  X  2550, 
we  might  use  a  very  hot  incandescent  filament  and  screen  out  by 


IONIZATION  PHENOMENA  21 

absorption  all  of  the  spectrum  except  those  wavelengths  thus 
obtaining  a  certain  "very  small  (c)  percentage  of  ultraviolet  light 
out  of  the  total  radiation  energy  of  the  incandescent  filament. 
We  then  employ  this  ultraviolet  light  to  generate  ozone  and  again 
obtain  a  certain  percentage  (d)  of  energy  transformation  which  in 
no  case  would  be  large.  The  total  efficiency  of  the  various  proc- 
esses is  almost  infinitesimally  small,  abed,  and  this  condition  is 
typical  of  the  generation  of  all  ionizing  agents. 

Not  only  is  the  efficiency  of  the  process  small  but  only  a  few  of 
all  the  possible  short  wavelengths  of  the  electromagnetic  radia- 
tions and  only  a  few  of  the  thousands  of  possible  atomistic  radia- 
tions at  comparatively  low  velocities  are  obtainable.  We  ought 
to  be  able  to  get  beams  of  gold  radiations  (charged  Au  atoms) 
possessing  any  velocity  we  wished  up  to  our  assumed  limit  of 
3(10) 10  cm.  per  sec.  We  might  wish  to  know  whether  the 
benzene  rings  would  remain  stable  for  all  possible  velocities. 
Would  these  radiations  resemble  the  beams  of  helium  ions  known 
as  a  rays? 

With  the  electron  radiations  we  are  more  successful.  In 
x-ray  tubes  we  can  generate  these  electrons  with  velocities 
approaching  that  of  light.  By  using  windows  these  electron 
radiations  can  be  utilized  outside  the  x-ray  tube.  But  even  here 
the  efficiency  of  generation  and  the  intensity  of  the  electron 
beams  are  small. 

The  generation  of  the  atomistic  radiations  has  only  been 
applicable  to  the  lighter  atoms  in  gases  at  low  pressures.  In 
vacuum  tubes  weak  radiations  of  the  gaseous  atoms  such  as  oxy- 
gen and  nitrogen  can  be  generated  with  varying  velocities 
approaching  say  a  tenth  that  of  light.  But  these  radiations  are 
easily  absorbed  by  any  material  that  can  be  used  as  a  window  for 
a  vacuum  tube  and  hence  only  very  weak  atomistic  radiations 
can  be  transmitted  outside  the  tube. 

Atomistic  radiations  homogenous  in  constitution,  magnitude  and 
direction  of  velocity  are  not  generated  in  gases  at  ordinary  pres- 
sures because  the  gases  do  not  support  an  electric  field  of  sufficient 
intensity.  As  soon  as  these  radiations  are  generated  they  begin 
to  transmit  their  energy  to  the  gas  molecules  during  collision  and 
this  prevents  the  acquirement  of  any  considerable  velocity  at  all. 

The  problem  of  generating  atomistic  radiations  will  be  greatly 
aided  by  the  use  of  very  high  voltages,  very  large  vacuum  tubes 
and  rapid  vacuum  pumps.  In  this  way  it  may  be  possible  to 


22  FUNDAMENTAL  PHYSICS 

produce  a  great  many  new  kinds  of  atomistic  aggregates  and  ions 
and  possibly  to  disintegrate  matter,  i.e.,  produce  artificial  radio- 
activity and  even  to  build  up  new  atoms.  Only  one  kind  of 
atomistic  radiation  possessing  a  high  velocity,  the  a  rays,  is 
known  and  on  account  of  its  being  ejected  by  a  number  of  radio- 
active products  it  is  assumed  to  be  a  component  part  possibly  of 
all  atoms.  The  question  of  the  philosopher's  stone,  of  learning 
the  structure  of  the  atoms,  of  analyzing  and  synthesizing  them  is 
to  be  answered  when  and  only  when  the  subject  of  atomistic 
radiations  has  been  fully  investigated. 


7.  THE  GATEWAYS  OF  KNOWLEDGE  AND  OUR 
*  SCIENTIFIC  DEVELOPMENT 

Every  one  of  us  receive  our  knowledge  through  the  sense 
organs  and  the  nervous  system  so  that  all  phenomena  of  the 
outside  world  are  received  by  the  mind  after  the  intricate  and 
not  well  understood  transformations  made  by  these  mechanisms. 
One  of  the  big  problems  of  science  consists  in  accurately  de- 
scribing these  transformations. 

It  follows  as  a  corollary  that  we  do  not  now  know  of  any 
"agent"  in  the  outside  world  except  in  terms  of  the  perceptions  of 
the  mind.  Revolutionary  as  scientific  discovery  has  been  we 
have  found  no  new  "agent"  in  nature.  At  one  time  x-rays 
were  thought  to  be  such  but  now  it  is  quite  certain  that  they  are 
electromagnetic  radiations.  If  x-rays  had  been  a  new  "agent" 
its  nature  would  have  remained  unknown  because  only  the 
properties  "felt"  by  our  senses  could  have  been  understood. 
It  is  for  this  reason  that  the  terms  electric,  magnetic  and  gravi- 
tational fields  of  force  mean  so  little  to  us  beyoncl  the  mechanical 
effects  which  they  produce.  An  illustration  of  this  kind  is 
given "  by  Bragg's  theory  of  x-rays  before  they  were  shown  to 
possess  the  same  diffractive  properties  as  light.  The  x-ray 
according  to  Bragg  was  an  "entity"  that  received  energy  from 
an  electron  striking  the  anticathode.  It  was  propagated  "with 
the  velocity  of  light"  just  as  a  "particle  of  matter."  In  this 
"entity"  stage  absolutely  nothing  was  known  of  the  x-ray 
except  as  a  carrier  of  energy.  When  x-rays  were  absorbed  by 
ionizing  a  gas  Bragg  assumed  that  the  "entity"  again  became 
an  electron  and  the  ionization  was  produced  by  the  electron. 
In  other  words  the  "entity"  stage  was  the  x  or  "unknown  ray 
state  acting  as  the  vehicle  of  the  electron's  energy. 

It  seems  probable  then  that  if  we  did  not  have  eyes  and  a 
temperature  sense  we  would  know  nothing  of  the  electromagnetic 

23 


24  FUNDAMENTAL  PHYSICS 

radiations  in  the  way  we  do.  It  would  indeed  be  very  interesting 
to  develop  a  philosophy  of  nature  ignoring  one  or  more  of  the 
"fundamental"  sense  elements  such  for  instance  as  inertia  or 
temperature.  , 

Our  evolution  as  a  race  and  as  individuals  has  contained 
determinative  factors  as  to  what  our  natural  philosophy  shall  be. 
The  flow  of  consciousness  in  ourselves  is  without  beginning  or 
end  (for  if  it  ends  we  of  course  cannot  know  it).  It  is  a  flow  of 
"entity"  elements  carried  into  the  main  channel  by  the  branch 
sources  of  the  sense  organs.  It  originates  in  its  womb  of  darkness 
and  hence  the  muscular  sensations — or  the  mechanistic  phi- 
losophy is  the  earliest  to  appear  and  remains  more  or  less  dominant 
through  life.  It  therefore  results  that  to  us  the  universe 
appears  as  a  mechanical  structure — a  world  of  forces.  The 
Newtonian  mechanics  need  not  give  us  the  laws  of  this  force 
world  necessarily  but  some  system  of  mechanical  forces  seems 
directed  by  our  origin  and  environment  as  the  guide  to  our 
natural  philosophy. 

It  is  reasonable  to  assume  that  by  opening  new  gateways  of 
knowledge  our  philosophy  would  be  entirely  changed.  We 
might  imagine  some  "field  of  force"  or  radiation  that  could 
directly  affect  the  molecular  processes  of  the  brain.  Molecules 
of  a  certain  type  could  be  introduced  into  the  brain.  Experi- 
ments for  example  have  been  made  where  a  person  was  placed 
in  an  intense  magnetic  field.  The  only  effect  seemed  to  be  a 
light  sensation  on  the  retina.  Some  day  there  may  however  be 
opened  to  us  a  world  of  melody  by  some  now  unknown  agent  of 
the  external  world  and  many  of  us  believe  that  a  future  life 
transforms  us  to  a  new  universe  of  phenomena  by  opening 
many  new  gateways  of  knowledge  and  by  freeing  us  from  'the 
incessant  molecular  changes  of  our  present  world. 

It  is  very  easy  then  for  us  to  picture  the  elements  of  the  mental 
world  freed  from  the  temporary  gateways  of  the  present  molecular 
systems  (nerves,  etc.)  and  opening  (through  systems  obeying 
the  law  of  conservation  of  properties)  into  the  ensembles  of  the 
"fundamental"  elements.  The  "disappearance"  of  the  mental 
elements  does  not  indicate  that  they  are  not  conserved  for  by 
analogy  this 'is  a  frequent  phenomenon  in  the  outside  world. 
As  the  ether  appears  as  the  reservoir  of  "lost"  but  conserved 
elements  of  the  outside  world  so  it  may  also  serve  for  the  mental 
elements. 


THE  GATEWAYS  OF  KNOWLEDGE          25 

To  continue,  the  course  of  our  training  and  the  development 
of  our  civilization  have  controlled  and  determined  the  course  of 
our  philosophy  just  as  environment  and  the  past  guides  the 
evolution  of  the  animals.  Our  words  carry  a  meaning  to  us 
long  before  we  know  of  forces  in  physics.  Our  arithmetic  and 
grammar  are  accepted  processes  in  any  theory  of  electricity 
which  we  may  develop  and  try  as  we  may  we  cannot  rebuild  any 
parts  of  our  natural  philosophy  without  at  least  using  some  of 
the  stones  of  the  previous  structures  which  had  been  erected. 
An  illustration  of  the  effect  of  grammar  upon  theoretical  physics 
is  sometimes  given  by  the  history  of  our  views  of  the  ether.  We 
had  discovered  the  wave  properties  of  light  and  we  could 
conceive  of  the  phenomena  only  as  the  undulating  motion  of 
some  medium.  As  a  verb  requires  a  noun  so  "to  undulate" 
required  a  subject  and  influenced  in  part  at  least  by  our  train- 
ing in  grammar  we  felt  and  many  feel  today  that  "the  ether 
undulates." 

As  a  result  one  finds  that  the  tactual  and  muscular  sensations 
predominate.  We  imagine  a  world  of  things  separated  by  dis- 
tances; these  things  may  be  portions  of  matter  that  we  can 
actually  touch  or  they  may  be  atoms  or  molecules.  Whatever 
they  are,  most  of  us  conceive  them  as  belonging  essentially  to  the 
realm  of  the  tactual  and  muscular.  Our  world  is  largely  one  of 
matter  in  motion,  a  c.g.s.  world.  But  why  should  the  concepts  of 
one  sense  seem  more  "fundamental"  to  us  than  those  of  another? 
Does  not  each  sense  organ  possess  its  own  peculiar  sensation 
concepts  and  are  not  each  of  these  concepts  of  the  same  theo- 
retical value?  Are  not  other  quantities  as  important  as  those 
indicated  by  the  senses?  Indeed  an  almost  infinitude  of  worlds 
are  possible  assuming  some  other  trinity  of  units  than  the  centi- 
meter, gram  and  second  as  being  the  predominate  ones. 

It  is  thus  possible  to  attribute  the  domination  of  some  sense 
concepts  by  others  as  being  due  to  the  fact  that  some  of  these 
concepts  have  been  much  more  important  to  us  in  our  develop- 
ment, both  as  individuals  and  as  a  race.  But  this  does  not  prove 
that  they  are  the  most  valuable  for  the  description  of  the  external 
world  and  that  they  should  therefore  possess  the  greater  scientific 
value. 

One  thus  comes  to  recognize  the  narrowness  of  many  of  our 
views  of  the  external  world  and  the  relation  between  the  world 
outside  the  senses  and  the  world  inside.  The  meaning  of  space, 


26  FUNDAMENTAL  PHYSICS 

time,  matter,  energy,  etc.,  are  dependent  upon  the  limited  ave- 
nues connecting  the  inner  and  outer  worlds.  We  can  easily  con- 
ceive of  a  means  of  communicating  between  these  worlds  directly 
without  the  aid  of  the  senses.  We  might  be  endowed  with  an 
entropy  sense;  a  sense  corresponding  to  any  thing  or  function  of 
things  and  changes  in  the  outside  world.  Then,  too,  could  not 
systems  in  the  mental  world  be  "tuned"  to  the  physical  world? 
And  may  not  this  "tuning"  be  accomplished  some  time  experi- 
mentally by  the  introduction  of  certain  atomic  or  molecular  sys- 
tems into  the  brain  as  is  done  with  the  digestive  tract  previous  to 
taking  x-ray  photographs. 

The  alphabet  of  the  language  we  select  to  describe  the  outside 
world  is  the  one  most  convenient  to  our  type  of  mind.  Another 
type  of  mind  might  use  an  entirely  different  alphabet  and  it 
sometimes  seems  reasonable  to  think  the  number  of  alphabets 
innumerable.  Our  ideas  as  to  the  convenience  of  any  given 
system  of  symbols  is  only  determined  by  the  present  state  of  our 
knowledge.  But  somehow  we  believe  we  are  ultimately  to  reach 
what  we  picture  is  "reality." 

We  continually  try  to  make  our  units  absolute  and  to  place  the 
"center  of  our  coordinate  axes"  at  a  place  suitable  to  natural 
phenomena  yet  somewhere,  someway  and  somehow  our  system  is 
largely  limited  by  our  past  experience  from  our  birth,  both  as 
individuals  and  as  races.  Nietzche  may  bring  us  a  strange  sys- 
tem but  he  has  simply  and  but  slightly  changed  either  the  origin 
or  the  bearings  of  philosophy.  So  we  in  our  efforts  to  make  a 
world  picture  of  phenomena  are  constantly  making  use  of  our 
past  experiences,  for  all  terms  must  be  interpreted  in  the  language 
of  experience.  Some  day  when  people  become  truly  scientific 
the  state  will  purposely  train  persons  to  obtain  as  varied  an  inter- 
pretation of  nature  and  life  as  possible.  Imagine  a  person  whose 
only  sense  was  hearing.  What  would  he  write  as  the  encyclo- 
paedia of  knowledge  ?  Compare  with  that  person  one  who  saw  the 
universe  by  means  of  any  electromagnetic  vibration,  who  pos- 
sessed a  sense  attune  to  the  electric  field  and  the  magnetic  field, 
who  could  "feel "  the  various  phases  of  each  molecular  impact  and 
we  get  some  appreciation  of  what  a  "broad  view"  of  our  world 
and  the  universe  should  be.  Our  advancement  in  science  will 
become  very  rapid  when  a  large  number  of  the  people  will  throw 
off  the  shackles  of  heredity  and  environment  and  develop  new 
"philosophies"  of  Truth.  Up  to  the  present  only  some  of  the 


THE  GATEWAYS  OF  KNOWLEDGE  27 

powers  of  a  very  few  individuals  directing  an  infinitesimal  portion 
of  the  wealth  of  society  have  endeavored  to  effectually  map  out 
the  Republic  of  Truth. 

By  sufficiently  correlating  our  sensation  stimuli  we  are  able 
to  find  a  source  for  all  the  stimuli  that  our  sense  organs 
receive. 

The  source  of  sensation  stimuli  may  be  defined  as  matter.  The 
means  by  which  these  stimuli  reach  our  sense  organs  are  "direct" 
(touch,  taste,  and  muscular  sensations)  and  "indirect"  (sight, 
sound) .  The  terms  direct  and  indirect  are  sufficiently  evident  to 
all  of  us.  But  how  are  stimuli  transmitted  by  the  indirect 
method?  Only  two  means  are  conceivable.  Either  the  indirect 
method  consists  of  particles,  entities  or  what  not,  passing  from 
the  source  of  the  stimulus  (i.e.,  matteV)  to  our  sense  organs,  par- 
ticles that  we  do  not  or  cannot  notice,  or  there  is  an  intervening 
medium  that  carries  the  means  that  affects  our  sense  organs. 
The  former  method  may  be  designated  as  the  "bullet"  type  of 
radiation  and  the  latter  as  the  "wave"  or  "pulse"  type  of  radia- 
tion. All  our  experience  is  unanimously  in  support  of  the  view 
that  it  is  impossible  for  us  to  receive  either  separate  or  direct 
sensation  stimuli -from  a  single  or  any  natural  group  of  "bullets  " 
or  direct  sensations  from  the  "medium"  itself  so  that  it  follows 
that  matter  must  be  the  source  of  all  radiations.  Neither 
the  "bullets"  nor  the  "medium"  can  therefore  consist  of 
matter  as  above  defined.  All  our  concepts  of  the  physical 
world  except  some  of  those  that  can  be  derived  by  the 
"direct"  method  of  sensation  must  be  correlated  by  the  use 
of  space,  the  element  necessitated  by  the  term  motion.  Our 
concepts  of  time,  space,  the  "ether,"  the  "electric,"  "mag- 
netic" and  "gravitational"  forces,  etc.,  are  plans  of  the 
physical  world  for  "explaining"  or  rather  correlating  and 
classifying  our  sensations. 

'  Our  present  work  is  largely  restricted  to  the  application  of  the 
"atomic"  theory  to  our  view  of  the  external  world.  Whenever 
we  obtain  sufficient  knowledge  concerning  any  concept  of  the 
external  world  so  as  to  be  able  to  apply  the  atomic  theory  to 
the  phenomena  representing  that  concept  then  that  concept 
ceases  to  be  merely  a  plan  and  becomes  something  finite  and 
discontinuous.  Terms  that  simply  represent  plans  of  the  exter- 
nal world  usually  possess  continuous  and  infinite  values.  Any 
quantitative  application  of  such  terms  to  the  external  world  or 


28  FUNDAMENTAL  PHYSICS 

of  anything  is  arbitrary.  There  can  be  no  natural  unit  of  time, 
of  space,  of  the  electrical  field  or  of  the  ether  until  these  quantities 
are  shown  to  be  atomic.  Concepts  that  are  merely  plans  of  the 
world  are  used  for  convenience.  When  these  terms  cease  to  be 
useful  they  are  discarded.  Any  term  representing  something 
in  the  world  that  possesses  an  atomic  composition  may  be  said 
to  be  "real,"  the  atoms  being  natural  units.  It  is  one  of  the  aims 
of  the  physicist  to  prove  an  "atomic"  composition  for  as  many 
physical  concepts  as  he  can. 

At  present  some  of  our  more  important  physical  concepts  are 
those  of  space,  time,  matter,  the  electric,  magnetic  and  gravi- 
tational fields  and  possibly  a  chemical  field  of  force.  Energy 
is  found  to  be  related  to  matter  or  vice  versa.  The  means  by 
which  energy  is  transmitted  from  one  portion  of  matter  to  another 
portion  is  by  three  methods,  the  "bullet,"  the  "medium"  and  the 
"direct  contact"  methods.  All  types  of  radiation  that  cannot 
be  shown  to  consist  of  moving  particles  of  matter  must  naturally 
be  included  in  the  "bullets"  or  the  "medium"  types  of  trans- 
mission. In  the  bullet  type  of  transmission  "entities"  or  ele- 
mentarquanta "  of  unknown  properties  must  carry  the  energy 
from  the  emitter  to  the  absorber.  In  the  medium  type  the  inter- 
vening medium  is  made  to  carry  the  energy  and  this  process 
necessitates  the  particles  of  the  medium  transferring  'the  energy 
from  one  to  the  other. 

Crudely  drawing  a  rough  analogy  between  the  humanistics 
and  the  natural  world  we  might  correlate  the  terms  money  and 
energy  and  people  and  matter.  The  elements  of  money  are 
cents,  of  energy,  radions,  of  people,  men  and  women,  and  of 
matter,  electrons  and  the  natural  atoms.  Money  in  the  pocket 
is  kinetic  energy  that  makes  "the  mare  go."  Relations  with 
other  people  result  in  the  interchange  of  the  circulating  medium. 
Money  in  a  bank  is  a  field  of  force  that  draws  men  to  or  away  from 
it  according  as  their  bank  account  is  positive  or  negative.  The 
marriage  of  a  positive  and  a  negative  ion  destroys  a  tremendous 
amount  of  kinetic  energy  of  pocket  change  as  those  old  neutral 
atoms  of  married  men  can  verify.  And  most  of  the  collision 
phenomena  of  individuals  can  be  or  at  least  is  attributed  by 
their  enemies  as  being  one  of  money  relations  or  forced  by 
future  hopes  of  this  variety.  So  it  is  that  terms  are  used 
in  "exact"  and  "fundamental"  science  and  in  the  other  affairs 
of  men. 


THE  GATEWAYS  OF  KNOWLEDGE 


29 


TRANSFORMATION  PROCESSES  OP  PHENOMENA 


Mental 
World 


Continuous  currents 
of  entities  in  the 
stream  of  time. 
By  analogy  many 
believe  that  cer- 
tain elements  in 
this  world  are  con- 
served as  in  the 
physical  world. 


Gateways  of 
Communication 

A  flow  of  entities  back 
•»  and  forth  between 
-  the  two  worlds  is 
brought  about  by 
energy  transforma- 
tions. "Angels"  are 
convenient  "ele- 
ments" hypothe- 
cated to  simplify, 
control  and  make  the 
transformations 
more  direct. 


The  Physical 
World 

Continuous  currents  of 
•>  entities  in  the  stream 
-  of  time  and  space. 
All  "laws"  indicate 
a  conservation  and 
n  o  n  d  isappearance 
of  certain  elements 
in  this  world  which 
can  therefore  be  de- 
fined as  the  "funda- 
mental ' '  elements . 
Eventually  our  con- 
venient elements 
(c.g.s.  elements)  will 
be  made  the  "funda- 
mental" elements. 

Because  the  elements  of  one  world  can  be  transformed  into 
elements  of  the  other  world  and  because  there  are  "fundamental" 
elements  in  the  physical  world  we  believe  that  these  remain 
conserved  during  their  transformation  and  hence  must  exist 
as  such  in  the  mental  world.  A  law  similar  to  the  second  law  of 
thermodynamics  could  intervene  by  making  the  flow  of  these 
fundamental  elements  such  that  they  would  eventually  reach  the 
reservoir  of  the  physical  world.  But  by  analogy  we  can  imagine 
"angels"  that  could  control  the  transformation  processes  and 
even  reverse  their  flow. 

The  above  assumption  that  all  the  phenomena  of  the  physical 
world  are  intelligible,  i.e.,  can  be  transformed  into  elements  of 
the  mental  world  and  vice  versa  and  that  all  these  elements  can 
be  derived  and  are  constructed  from  a  few  fundamental  elements 
that  are  conserved  (i.e.,  are  indestructible)  may  be  assumed  as 
a  system  of  philosophy,  the  "source,"  "base"  and  "ending" 
of  the  system  being  the  fundamental  elements. 

As  the  "elements"  of  the  mental  world  are  obtained  from  the 
transformation  of  "elements"  of  the  conserved  ensemble  we 
will  assume  that  the  laws  of  this  ensemble  apply  to  both  realms. 

Law  1. — There  is  a  conserved  nondisappearing  ensemble  of 
mental  elements  in  which  an  electrical  element  is  "absolutely" 
conserved. 

Law  2. — The  equations  of  transformation  between  the  "ele- 
ments" possess  a  natural  direction  of  flow. 


30  FUNDAMENTAL  PHYSICS 

Law  3. — The  "medium"  provides  the  only  means  for  this 
flow  of  transformations. 

To  summarize  we  have  transformations  in  the  Newtonian 
world  brought  about  during  "collisions"  or  the  "contact"  of 
magnitudes  of  ordinary  matter.  Apparently  the  ether  does  not 
function  in  these  transformations,  at  any  rate  the  "contact" 
of  two  portions  of  matter  is  the  necessary  and  sufficient  condition 
and  "free  space"  is  a  perfect  screen  in  preventing  the  inter- 
changes. The  senses  of  touch,  taste,  smell,  hearing  and  the 
muscular  sense  apparently  operate  by  the  contact  process.  Our 
individual  and  racial  growth  has  founded  our  knowledge  very 
largely  upon  a  Newtonian  philosophy. 

The  transformations  which  take  place  through  the  ether  and 
whose  emission  and  absorption  are  largely  if  not  entirely  "elec- 
trical" (such  as  light  and  heat)  are  observed  through  the  eyes 
and  the  temperature  sense.  How  the  nerves  transform  these 
sensations  before  they  reach  the  brain  we  do  not  know  though 
they  appear  to  be  at  least  partly  electrical.  This  condition 
affords  the  hope  that  the  mind  can  be  reached  directly  or  in- 
directly by  other  electrical  methods  and  that  new  channels  of 
information  to  the  mind  may  be  discovered.  This  view  is 
especially  inviting  if  the  mental  processes  themselves  are  electrical 
rather  than  Newtonian,  the  chemical  changes  being  regarded  as 
largely  electrical. 

The  mental  world  then,  is  pictured  as  an  ensemble  of  the 
fundamental  elements  of  the  natural  world  directed  by  angel 
elements  of  which  we,  as  individuals,  are  entity  systems.  We 
may  assume  that  angels  may  possess  as  fine  grained  a  structure 
as  the  natural  entities,  and  that  the  angel  elements  are  as 
certainly  conserved  and  nondisappearing,  though  as  subject 
to  transformation,  as  are  the  elements  of  the  natural  world. 
Should  we  care  to  do  so  the  electrical  attributes  of  the  positive 
and  negative  could  be  assigned  to  the  mental  elements  as  they 
have  been  to  ordinary  matter  and  the  ether  thus  making  a 
complete  parallelism  in  this  triune  ensemble. 


8.  SOME  PROBLEMS  IN  PHYSICS 

The  new  science  started  in  geometry.  It  appeared  as  an 
analysis  of  the  axioms  assumed  by  Euclid.  We  may  consider  the 
three  geometries  to  be  based  on  the  view  that  the  angles  of  a 
triangle  are  equal  to,  greater  than  or  less  than  two  right  angles 
and  develop  the  three  consistent  systems  of  geometry  for 
Euclidean,  hyperbolic  and  elliptic  space.  The  new  science 
movement  consists  of  a  thorough  criticism  of  the  axioms  or 
"fundamental"  "elements"  of  any  branch  of  knowledge,  the 
development  of  as  many  consistent  treatments  or  "systems" 
of  knowledge  as  the  fundamental  elements  permit  and  then 
comparing  these  systems  to  reality  by  the  most  exacting  and 
comprehensive  empirical  methods  available. 

Applied  to  natural  phenomena  the  new  science  applies  the 
keenest  analysis  possible  of  the  methods,  apparatus  and  the 
units  of  measurement.  From  the  "laws"  of  nature  it  de- 
velops as  many  consistent  systems  of  science  as  are  possible. 
That  system  (applied  perhaps  in  many  ways  directly  and  in- 
directly) which  agrees  "at  every  angle"  with  "reality"  when 
tested  experimentally,  is  then  accepted.  In  natural  philosophy 
the  branch  of  relativity  exemplifies  the  nature  of  the  new  science, 
the  problems  which  it  faces  and  the  methods  which  it  employs  to 
answer  them. 

That  the  development  of  the  new  science  is  extremely  difficult, 
will  be  recognized  as  soon  as  we  enter  the  laboratory.  Let 
us  assume  that  our  physicist  is  to  demonstrate  the  measurement 
of  the  unit  of  electric  charge  before  a  Pharaoh,  who  has  set  out 
to  develop  the  new  science  of  electricity.  No  metrical  instru- 
ments are  available  so  that  convenient  units  must  be  selected. 
(1)  A  convenient  length  is  chosen  and  used  as  a  standard;  (2) 
the  Newtonian  or  some  similar  type  of  mechanics  is  carried 
sufficiently  far  to  define  and  measure  forces;  (3)  electric  charges 
are  generated  and  disposed  so  that  they  simulate  point  charges; 
(4)  a  method  of  measuring  electrical  charges  is  devised  and  a 
"definition"  and  a  method  of  obtaining  two  "equal"  electrical 

31 


32  FUNDAMENTAL  PHYSICS 

charges  is  agreed  upon;  (5)  Coulomb's  law  that  the  force  (F) 
of  repulsion  of  two  charges  (d,  e^)  when  placed  at  a  distance  r 

from  each  other  is  F  =  -r-f  is  obtained  experimentally. 

K/T 

(6)  The  law  F  =  -j-\  must  be  verified  as  being  consistent  with 

all  phenomena  as  they  may  be  known  in  the  realm  of  Pharaoh. 
The  law  is  then  assumed  to  be  "  universal."  (7)  The  magnitude 
of  the  charges  is  independent  of  the  kind  of  matter  with  which 
they  may  be  associated;  (8)  the  temperature;  (9)  the  kind  of 
matter  along  r;  (10)  the  presence  of  a  magnetic  field;  (11)  the 
earth's  gravity  field;  (12)  the  rotation  of  the  earth  or  its  motion 
in  space;  (13)  k  is  assumed  to  be  a  constant;  (14)  the  force  F 
is  assumed  to  be  independent  of  the  streams  of  energy  flowing 
about  the  charges. 

(15)  After  having  subjected  Coulomb's  law  to  a  thorough 
investigation  of  which  the  above  is  but  a  very  superficial  analy- 
sis and  having  found  it  to  be  consistent  with  the  ideas  of 
Pharaoh,  we  employ  it  to  define  the  unit  of  electric  charge. 
Two  "  equal"  "  point"  charges  of  electricity,  each  possesses  unit 
magnitude  when  they  repel  each  other  with  a  force  of  one  dyne 
when  separated  a  distance  of  one  centimeter  in  a  medium  whose 
dielectric  constant  is  unity. 

The  difficulties  of  the  new  science  can  be  the  better  appreciated 
when  Pharaoh  asks  if  these  conditions  apply  to  two  electrons 
carried  along  by  the  front  of  a  light  wave;  by  two  electrons 
existing  in  the  center  of  the  sun;  by  two  electrons  rotating  in 
a  uranium  atom;  or  by  two  electrons  in  the  brain  of  a  person 
swept  by  the  thought  storms  of  "new"  science. 

Yet  the  difficulties  of  applying  the  philosophy  of  the  new  sci- 
ence to  natural  phenomena  are  not  as  appalling  as  we  might  at 
first  expect,  and  this  condition  is  due  to  the  most  marvelous 
simplicity  of  natural  phenomena.  If  there  is  any  reason  for 
optimism  and  for  faith  it  lies  in  our  being  able  to  successfully 
apply  the  new  science  to  phenomena  unreachable  to  our  sense 
organs  and  to  find  that  the  fundamental  elements  of  these 
phenomena  are  extremely  simple  and  apparently  form  a  single 
consistent  system. 

We  have  only  to  point  to  the  complex  phenomena  of  elec- 
tricity. So  far  as  our  knowledge  extends  all  electrical  phe- 
nomena can  be  consistently  explained  by  means  of  the  electron 


SOME  PROBLEMS  IN  PHYSICS  33 

and  natural  atoms.  The  hidden  shadow  of  this  is  the  positive 
charge  denoted  as  the  positive  electron.  Like  "  potential "  energy 
the  positive  electron  is  assumed  to  explain  the  disappearance 
of  the  negative  electron. 

The  "single  consistent  system"  is  denoted  as  the  natural 
philosophy  of  the  new  science.  The  new  science  asserts  that 
there  is  an  ensemble  of  fundamental  elements  in  the  universe  and 
that  all  natural  phenomena  consist  in  the  transformations  of 
the  fundamental  elements  according  to  laws  which  it  is  the  prob- 
lem of  science  to  ascertain.  With  a  knowledge  of  the  fundamen- 
tal elements,  the  laws  of  the  system  and  a  certain  "locus"  of 
conditions,  the  whole  universe  system  can  be  mapped.  It  is  the 
aim  of  the  new  science  to  so  map  all  natural  phenomena  and  then 
to  test  these  results  experimentally. 

The  modus  operandi  of  this  tremendous  task  is  that  of  divid- 
ing the  universe  into  entity  assemblages.  In  any  entity  as- 
semblage phenomena  may  be  considered  as  forming  a  system 
where  a  common  "atmosphere"  prevails.  As  an  example  we 
may  consider  the  ordinary  earth  phenomena  to  form  an  entity 
assemblage  where  Newton's  laws  of  motion  consistently  apply. 
There  is  the  atmosphere  of  Newtonian  mechanics  everywhere 
pervading  the  assemblage.  It  of  course  follows  that  the  entity 
assemblage  will  be  determined  largely  by  the  point  of  view. 
We  shall  view  phenomena  in  terms  of  the  apparatus,  convenient 
units,  methods  of  observing  and  laws  of  physics  required  to  map 
them  as  the  factors  determining  the  entities. 

The  procedure  will  be  that  of  developing  a  consistent  and  con- 
venient system  of  physics  for  each  entity  assemblage.  The 
ensemble  of  entity  assemblages  will  then  be  considered  with  a 
view  of  adopting  a  single  universal  system  of  physics.  When 
this  work  has  been  successfully  completed  the  new  science  of 
physics  will  be  the  result. 


9.  THE  DIRECTED  ELEMENTS 

Amongst  the  elements  that  are  necessary  in  the  development 
of  a  science  employing  geometrical  processes  are  those  that 
possess  the  quality  of  direction.  In  the  Newtonian  mechanics 
rigid  bodies  are  well  suited  for  defining  directions  as  the  parts 
can  be  marked  and  a  set  of  coordinate  axes  established  with  com- 
parative ease.  But  when  the  simpler  ensembles  of  natural  ele- 
ments such  as  rapidly  moving  electrical  charges  and  the  ether  are 
to  be  given  a  geometrical  interpretation  the  problem  of  defining 
direction  and  of  measuring  elements  that  possess  a  directive 
quality  is  very  different. 

The  natural  direction  most  used  in  the  past  has  been  that  of 
the  axis  of  rotation  of  the  earth.  Knowing  that  this  axis  is 
subject  to  a  certain  amount  of  wobbling,  the  North  Pole  star 
has  been  used  to  define  direction.  But  it  is  fully  understood 
that  this  "north"  direction  is  not  constant  or  absolute  when  so 
defined.  It  is  then  natural  to  hunt  through  the  entity  systems 
of  nature  to  see  if  in  any  sense  direction  can  be  absolutely  defined 
or  if  it  will  always  be  necessary  to  speak  of  direction  in  a  local 
sense  and  employ  that  local  direction  (such  as  that  of  the  earth's 
axis)  that  is  most  convenient  for  our  purpose. 

Of  the  "directed"  quantities  it  appears  that  the  ether  states 
such  as  the  electrical,  magnetic  and  gravitational  fields  possess 
somewhat-  similar  "directive"  properties.  The  gravitational 
"direction"  is  unidirectional  in  that  a  mass  always  experiences 
the  same  directive  effect  whereas  the  electric  and  magnetic 
fields  exert  reversed  directive  effects  according  as  a  plus  or  nega- 
tive and  a  north  or  south  magnetic  pole  is  placed  in  the  field. 
Ordinarily  the  "direction"  quality  of  the  electric  field  is  assumed 
fixed  the  same  as  it  is  for  the  gravitational  field.  We  may  go 
so  far  as  to  consider  the  physical  world  as  possessing  a  certain 
number  of  direction  "elements"  and  that  these  elements  may 
possess  an  "atomic"  structure. 

The  elements  that  appear  with  directive  properties  include 
electric  charge,  natural  matter,  time  and  length  if  defined  by 
means  of  a  rigid  lattice  structure  such  as  possessed  by  crystals 

34 


THE  DIRECTED  ELEMENTS  35 

and  assumed  for  a  "latticed"  ether.  If  our  lattice  structure  is 
not  isotropic,  this  property  serves  to  define  direction  also.  Some 
of  these  directed  qualities  resemble  the  series  of  positive  and 
negative  numbers  in  that  the  sum  of  a  "negative"  and  a  "posi- 
tive" unit  results  in  a  disappearance  of  both  units.  Directed 
qualities  of  this  type  may  aid  in  defining  an  origin  for  an  ensem- 
ble. Other  magnitudes  such  as  temperature,  mass  and  entropy 
do  not  possess  "negative"  values. 

There  are  certain  systems  that  appear  to  possess  "absolutely" 
directed  quantities.  We  can  imagine  a  system  of  science  de- 
veloped in  the  interior  of  a  crystal  (placed  in  a  liquid)  for  which 
an  "absolute"  origin  of  space  coordinates  could  be  defined  that 
would  introduce  a  symmetry  into  phenomena  that  would  other- 
wise not  be  possible.  The  lattice  work  of  the  crystal  would  pro- 
vide a  means  of  defining  "direction"  in  an  "absolute"  manner 
especially  if  the  crystal  lattice  work  is  not  isotropic.  The  most 
symmetrical  form  of  physics  that  could  be  developed  would 
apparently  be  that  in  which  the  center  of  the  crystal  would  be 
the  origin  of  the  coordinate  axes.  The  "direction"  of  any 
atom  from  the  origin  in  the  lattice  work  could  be  defined  as  so 
many  "lattice"  spaces  along  each  one  of  the  crystalline  axes. 
If  the  minimum  length  of  measurement  was  the  distance  be- 
tween two  neighboring  lattice  elements,  then  the  "atomic" 
angle  of  "direction"  would  be  that  subtended  by  a  lattice  ele- 
ment at  the  boundary  of  the  crystal. 

The  number  of  independently  "directed"  elements  of  the  phys- 
ical universe  may  aid  in  indicating  the  number  and  nature  of 
the  "fundamental  units"  of  science.  The  number  of  "direc- 
tions" may  give  the  degree  of  the  manifold  of  phenomena. 
Thus  we  may  agree  that  the  ether  fields  of  force  give  us  the  three 
"directions"  of  extension,  the  succession  of  events  gives  us  the 
"direction"  of  time  and  the  entropy  and  radioactive  changes 
give  us  the  "direction"  or  the  "running"  down  of  the  universe. 
If  these  could  be  considered  as  fundamental  and  independent 
"direction"  elements  just  as  length,  mass  and  electric  charge 
have  been  considered  as  fundamental  physical  elements  then 
the  universe  "space"  would  consist  of  five  dimensions  and  phys- 
ical transformations  would  take  place  in  a  5-manifold.  The 
degree  of  the  manifold  will  determine  the  nature  of  the  geometry 
to  be  adopted. 

Let  us  assume  that  the  physical  space  is  to  be  defined  by  ul- 


36  FUNDAMENTAL  PHYSICS 

timate  and  directed  elements  that  are  conserved  and  never  dis- 
appear. Let  us  assume  a  lattice  type  of  an  absolutely  stagnant 
ether  and  that  the  magnitudes  of  the  axial  quantities  are  to  pos- 
sess positive  and  negative  characteristics.  An  arbitrary  origin 
and]direction  is  marked  on  the  lattice  work.  A  stream  of  radia- 
tion is  directed  so  that  its  energy  flow  is  along  that  of  the  arbi- 
trary axis.  The  electric  and  magnetic  vectors  of  this  radiation 
stream  could  be  assumed  to  define  two  more  axes;  an  electric 
charge  and  a  time  axis  could  be  added  thus  constituting  a  5- 
manifold  space.  On  account  of  the  universal  existence  of  the 
ether  in  all  entity  systems  it  seems  most  promising  to  expect 
any  absolute  definition  of  directed  elements  to  be  made  with  ref- 
erence to  the  structure  of  the  ether.  Up  to  the  present  all 
definitions  of  this  sort  have  been  local  and  except  for  the  ether 
there  appears  no  other  base  for  a  universal  science.  It  is  for 
this  reason  that  the  transformation  of  the  direction  properties 
of  any  magnitude  from  one  ensemble  to  another  is  very  difficult. 
We  can  picture  the  energy  changes  and  atomize  the  direction 
qualities  that  enter  into  these  changes  by  assuming  radion 
elements  for  the  elementarquanta.  These  radions  contain  the 
elements  of  directed  energy.  To  give  extension  there  is  assumed 
six  types  of  radions,  a  type  for  each  quadrant,  there  being  positive 
and  negative  radions  whose  oppositely  directed  energy  neutral- 
izes with  the  result  that  any  element  containing  these  two 
elements  would  be  at  rest.  The  radions  could  be  considered  as 
as  ±  rx,  ±  ry  and  ±rz.  The  motion  of  any  body  could  be 
described  as  being  due  to  its  containing  a  given  number  of  these 
radion  elements  in  the  way  that  we  describe  motions  and  forces 
by  considering  the  projected  components  on  the  axes.  Colli- 
sions would  be  described  by  the  interchange  of  radions.  Fields 
of  force  would  be  regions  where  a  certain  type  of  radion  pre- 
dominated and  matter,  charge  and  the  ether  would  be  the 
vehicles  of  radions.  We  could  assume  the  radions  to  be  con- 
served and  to  be  the  ultimate  energy  elements.  The  assumed 
positive  and  negative  characteristics  of  charge,  natural  matter 
and  the  electroethons  could  be  attributed  to  the  radions.  A 
reason  for  not  attributing  these  energy  properties  to  the  ether 
is  that  the,  ether  is  frequently  assigned  a  stagnant  quality  when 
we  wish  to  define  direction  absolutely.  This  objection  is  removed 
however,  when  we  consider  the  energy  direction  of  the  radions 
to  be  conserved. 


THE  DIRECTED  ELEMENTS  37 

If,  then,  energy  can  all  be  considered  to  be  kinetic  and  the 
trend  of  modern  discovery  supports  this  view,  it  is  possible 
to  believe  that  all  directed  quantities  may  consist  of  three 
elements.  A  quantity  such  as  time  may  be  the  measure  of 
energy  changes  and  therefore  a  function  of  other  quantities. 
,  The  theory  of  relativity  indicates  that  we  can  only  determine 
relative  motion  and  that  in  the  case  of  rotation,  we  can  say, 
that  if  our  universe  was  set  rotating,  the  physical  laws  would 
be  changed. 


10.  THE  GENERAL  ENTITY  VIEW  OF  THE  UNIVERSE 

In  taking  a  survey  of  phenomena  we  find  that  there  are  systems 
that  are  more  or  less  complete  in  themselves  and  to  a  great  degreei 
isolated  from  each  other.  These  systems  are  invariably  com- 
posed of  similar  parts,  individuals,  groups,  atoms  or  entities  as 
we  may  wish  to  name  them.  This  universal  condition  is  de- 
scribed as  the  entity  view  of  the  universe.  To  be  seen  in  a  clear 
light  the  entity  structure  of  any  system  must  be  observed  from 
a  finer  grained  system  than  the  system  under  observation. 
From  our  every  day  world  water  may  be  considered  as  a  continu- 
ous fluid  and  its  behavior  can  be  accurately  described  by  hydro- 
dynamical  equations  assuming  that  water  is  a  perfect  fluid. 
Viewed  from  the  electron  world  however,  water  consists  mostly 
of  space  filled  at  rare  intervals  with  whirling  electrons  and  the 
positive  nuclei  of  hydrogen  and  oxygen  atoms. 

The  entity  or  atomic  theory  of  phenomena  has  been  found  to 
be  universal  and  applicable  everywhere  if  a  finer  grained  system 
could  be  employed  in  the  laboratory  than  the  one  under  observa- 
tion. Experience  would  therefore  lead  us  to  consider  all  systems 
as  constituted  of  entities.  The  second  experimental  law  of  the 
entity  structure  of  systems  is  that  the  number  of  different 
entity  elements  becomes  less  as  the  system  becomes  finer  grained. 
The  complete  entity  view  would  then  lead  us  to  consider  the 
finest  grained  system  as  consisting  of  a  single  entity  element. 

(a)  The  large  star  and  nebulae  systems  that  drift  in  groups 
through  space  probably  give  us  our  coarsest  grained  system  with 
the  stars  as  entity  elements.  The  adaptation  of  the  laboratory 
and  the  units  to  suit  the  system  is  very  well  illustrated  by  the 
use  of  the  light  year  as  the  unit  of  length  for  this  system. 

A  few  relations  appear  among  the  stars  and  the  nebulae.  The 
redder  and  apparently  "older"  stars  and  a  class  of  nebulae  possess 
greater  velocities  than  the  hotter  stars.  An  effect,  such  as  a 
differential  light  pressure  on  a  moving  star,  might  result  in  a 
star  system  increasing  its  velocity  as  it  grew  older.  The  universal 
appearance  of  substances,  such  as  hydrogen,  sodium,  calcium 
and  iron  in  the  star  systems,  indicates  a  common  atomic  constitu- 
tion of  the  universe,  and  the  view  is  that  the  universal  existence 
of  this  form  of  matter  is  due  to  similar  boundary  conditions 

38 


GENERAL  ENTITY  VIEW  OF  THE  UNIVERSE  39 

with  the  ether,  rather  than  to  any  intercommunication  of  this 
matter  between  the  stars.  These  forms  of  matter  have  been 
genetically  formed  in  situ  in  the  particular  entity  system  from 
the  ether  and  the  elements  that  the  ether  can  transmit,  such  as 
the  electromagnetic  vibrations.  The  origin  of  a  star  center 
may  even  be  cyclonic,  starting  from  a  peculiarly  unstable  condi- 
tion of  the  medium. 

The  sorting  that  takes  place  in  an  entity  system,  is  illustrated 
by  the  appearance  of  spectra  in  the  nebulae  and  nebulous  stars 
that  are  unknown  on  the  earth.  Were  it  not  for  "low 
temperature"  compounds,  such  as  water  and  the  radioactive 
elements,  hydrogen  and  probably  helium,  would  be  unknown 
to  us.  Assuming  the  width  of  spectrum  lines  to  vary  as  the 
square  root  of  absolute  temperature,  Buisson  and  Fabry  have 
found  the  "  temperature  "  of  the  Orion,  nebula  to  be  about  15,000°. 

(6)  Our  solar  system  with  entity  .elements  of  the  planets, 
satellites,  and  comets  is  probably  the  best  ordered  entity  system 
known  and  the  most  accurately  described  at  the  present  time. 
Undoubtedly  this  system  as  a  whole  is  one  of  the  atoms  in  a 
star  system.  The  almost  perfect  ordering  of  the  system  is 
due  to  its  being  in  a  steady  gravitational  state.  Only  collisions 
with  minute  particles  in  space  occur.  We  have  only  to  imagine 
collisions  with  similar  systems  to  obtain  a  very  disordered  condi- 
tion. The  atomic  elements  of  matter  can  be  compared  with 
'much  profit  to  our  solar  system,  the  " emptiness"  of  space  inside 
of  the  atoms  being  even  more  pronounced  than  is  the  case  of  our 
solar  system. 

(c)  The  phenomena  that  take  place  on  the  planets  and  the 
sun  such  as  sun  spots,  storms  or  the  formation  of  water  streams  or 
islands  are  extremely  disordered  though  there  may  appear  similar 
entity  elements.  These  elements  are  short  lived.  It  may  be 
stated  that  in  general  the  ordering  and  simplicity  of  any  entity 
system  is  proportional  to  the  life  period  of  the  entity  elements. 
In  the  planetary  systems  many  of  the  phenomena  are  of  the  cy- 
clone variety  in  that  their  origin  is  more  or  less  sporadic  and  due 
to  a  play  of  forces  that  are  infinitesimal  compared  to  those  de- 
veloped at  a  later  stage.  Once  started  the  cyclone  type  of  phe- 
nomena possesses  a  track  or  life  that  is  at  least  partly  amenable 
to  mathematical  treatment  and  prediction  but  their  birth  can- 
not be  very  accurately  predicted. 

Cyclone  phenomena  differ  from  the  trigger  type  in  that  the 


40  FUNDAMENTAL  PHYSICS 

latter   possess   a  greater   degree   of   uniformity  and  owe  their 
origin  to  a  source  usually  outside  of  the  system. 

(d)  Animal  and  plant  life  illustrate  atomic  structure  very  well 
in  that  the  individual  plants  and  animals  may  be  considered  as 
the  natural  units  with  the  cell  to  be  the  universal  elemental 
unit  in  this  whole  kingdom  of  life.     Like  the  atoms  of  matter 
the  cell  possesses  a  structure. 

The  world  of  life  presents  its  individual  units  with  certain 
polar  characteristics  of  sex  which  may  be  pictured  as  the  fading 
out  of  the  very  pronounced  polar  characteristics  of  electrical 
and  magnetic  entities  and  of  the  natural  atoms  of  matter.  Many 
chemists  speak  of  valency  as  possessing  polar  characteristics 
and  it  is  only  natural  to  expect  that  if  the  life  entities  are  the  con- 
tinuation of  the  series  of  the  molecular  systems  then  the  polar 
characteristics  not  only  of  the  physical  life  of  the  individuals  but 
also  of  the  mental  and  the  moral  atmospheres  of  these  entities 
may  be  the  glimmering  traces  flowing  from  those  extremely  fine 
grained  entity  systems  where  these  properties  are  so  pronounced. 

The  operation  of  illy  defined  forces  to  produce  entity  systems 
is  illustrated  in  the  university.  A  man  must  be  either  a  chemist 
or  a  psychologist  or  some  other  type  of  entitist  or  else  he  finds 
himself  alone,  ostracized  and  running  little  chance  of  securing  a 
stable  position  in  the  satellite  electrons  that  are  drawn  to  the  nu- 
cleus president  and  board  of  trustees  by  the  financial  forces. 
The  brilliancy  of  illuminating  knowledge  to  the  surrounding 
spaces  of  ignorance  and  the  reception  of  all  the  hard  blows  of 
collisions  is  the  function  of  the  satellite  electron  teachers  while  all 
the  force  of  the  system  is  held  by  the  central  nucleus.  And  if 
the  system  is  subjected  to  outside  criticism  the  divine  rights  of 
the  central  powers  complacently  permits  of  the  ejection  of  one 
or  more  of  the  outer  electrons.  So  we  perceive  the  faint  echoes  of 
the  elementary  material  systems  resounding  in  the  clash*  and  din 
of  the  far  removed  entities  in  the  realms  of  life,  even  in  the  sacred 
institutions  of  learning. 

(e)  The  molecular  systems  form  the  natural  units  of  our  or- 
dinary world.     The  molecules  are  the  units  of  neutral  or  or- 
dinary matter  and  they  constitute  the  natural  frontiers  of  the 
realm  of  Newtonian  mechanics.     The  treatment  and  laws  of 
solids,  liquids  and  gases  is  essentially  the  science  of  molecules  and 
comparatively  small  molecular  systems.     An  exact  and  complete 
molecular   science,    a    full    understanding    of   life   phenomena, 


GENERAL  ENTITY  VIEW  OF  THE  UNIVERSE  41 

the  discovery  of  the  missing  links  between  the  life  elements  and 
the  molecules  and  the  practical  acquirement  of  the  powers  of 
the  angels  to  control  molecular  and  life  transformations  remain 
as  some  of  the  fundamental  problems  for  state  and  other  social 
organizations  to  grapple  with  their  full  energies. 

(/)  The  chemical  world  lies  between  the  boundaries  of  the  mo- 
lecular and  atomic  worlds.  Many  claim  that  the  transformations 
that  take  place  here  are  essentially  electrical  while  others-postu- 
late chemical  "fields"  of  force  of  an  elementary  nature.  The 
very  nature  of  these  claims  emphasizes  the  tremendous  field 
here  inviting  research  work.  The  backward  state  of  our  knowl- 
edge of  chemistry  is  due  to  our  not  being  able  to  experiment 
with  individual  chemical  reactions  and  for  the  reason  that  these 
reactions  are  extremely  variable  and  are  short  "collision"  phe- 
nomena rather  than  conditions  of  long  steady  states  such  as  is 
exemplified  by  our  solar  system. 

(g)  The  atomic  world  is  described  in  a  separate  chapter  and  the 
ionization  world  has  been  briefly  treated.  The  Newtonian 
philosophy  no  longer  applies  and  another  science  arises.  The 
world  of  the  electrons  and  the  natural  atoms  is  essentially  an 
electrical  world.  The  world  of  ordinary  "contacts"  ends.  The 
muscular  senses  are  dumb.  There  is  no  tactual  touch  to  these 
phenomena.  -This  is  the  world  of  the  eye  and  of  radiations. 
This  is  the  world  of  the  "  radions, "  electricity,  magnetism,  natural 
atoms  and  the  ether.  A  new  philosophy  reigns.  We  may  call 
this  the  electrical  philosophy  and  it  has  to  do  with  electrons  and 
the  "natural"  atoms. 

Almost  a  science  has  developed  concerning  the  family  groups 
of  the  periodic  system  of  the  natural  atoms.  The  radioactivity 
of  the  heavier  atoms  has  shed  much  light  upon  these  family 
relations  in  a  genetic  sense  and  future  experiments  promise  to 
show  that  the  92  natural  atoms  may  possess  as  simple  a  consti- 
tution as  electrical  charges.  The  life  history  of  the  stars  is 
closely  associated  with  the  birth  and  death  of  the  natural" atoms. 

(h)  The  subatomic  world  is  sketched  under  the  structure  of 
the  atoms.  This  region  remains  almost  entirely  for  future  ex- 
ploitation as  does  the  (i)  radiation  entity  systems  and  (j)  the 
ether.  We  presume  that  the  relative  "grain"  or  fineness  of 
structure  of  these  entity  systems  is  roughly  as  given:  (a)  Star 
clusters;  (6)  suns;  (c)  "cyclones"  (temporary);  (d)  living  beings 
(temporary?);  (e)  molecules;  (/)  neutral  atoms;  (g)  electrons  and 
natural  atoms;  (A) ^helium  nuclei;  (i)  ether  electroethons  and 


42  FUNDAMENTAL  PHYSICS 

(j)  radions.  The  i  and  j  groups  can  be  given  their  mathemat- 
ical significance  of  imaginary  quantities. 

So  much  for  the  existence  of  entities  in  the  natural  world. 
As  you  read  this  page  your  eye  crosses  it  in  jerks;  each  jerk  in 
a  way  being  transformed  into  a  thought  entity.  A  thought 
entity,  a  phrase  or  a  word  may  be  considered  as  a  molecule  or 
an  aggregate,  this  latter  being  constructed  of  words,  the  simple 
molecules  and  ultimately  of  letters,  the  atoms  of  our  thought 
structures.  Our  number  system  is  even  simpler,  all  numbers 
("molecules")  being  formed  from  nine  elementary  atoms.  Our 
music  is  also  based  on  a  few  notes  covering  only  several  octaves. 

In  a  way  each  thought  of  the  outside  world  is  an  entity  corre- 
sponding to  an  assumed  entity  in  the  natural  world.  Our  sci- 
ence has  shown  that  the  elementary  entities  (electrons  and  atoms) 
of  the  outside  world  are  almost  as  simple  as  our  atom  letters. 
In  addition  as  the  entities  become  infinitesimal  and  of  a  lower 
order  the  units  are  found  to  become  simpler.  The  means  of  com- 
munication of  energy  between  the  larger  order  of  units  (suns) 
seems  to  be  the  same  as  that  between  the  smallest  units  (atoms, 
electrons,  atom  nuclei),  thus  leading  us  to  believe  that  all  inter- 
communication between  entity  systems  must  be  by  means  of  the 
ether  electromagnetic  processes. 

The  entity  philosophy  is  indeed  of  a  very  wide  and  subtle 
application  on  account  of  our  mental  process.  Any  thought 
entity  based  upon  knowledge  of  the  outside  world  can  be  ap- 
plied to  that  knowledge  so  that  innumerable  entities  may  be  as- 
sumed. Any  physical  magnitude  may  thus  be  assumed  to  possess 
an  atomic  structure  and  the  assumption  made  a  natural  hypo- 
thesis to  be  tested  by  experiment.  And  if  the  ultimate  elements 
of  the  physical  world  are  atomic  in  nature,  presumably  all  phys- 
ical magnitudes  will  at  least  ultimately  be  found  to  possess 
an  atomic  structure.  Our  fundamental  units  will  however  be 
those  of  nature.  For  example  the  ultimate  unit  of  time  would  be 
the  shortest  periodic  occurrence  in  nature  that  can  be  observed, 
the  unit  of  length,  the  shortest  physical  entity  that  can  be  used  as 
a  measuring  bar  and  the  -unit  of  mass,  the  smallest  mass  entity 
that  can  be  separated  from  other  masses. 

The  general  entity  theory  of  nature  also  asserts  that  every 
measurement  of  natural  phenomena  must  yield  a  rational  in- 
tegral number  when  the  natural  entity  elements  are  employed 
as  units.  All  natural  phenomena  are  granular  and  ratios  of  all 
natural  quantities  may  be  commensurable. 


11.  THE  ATOMIC  STRUCTURE  OF  MATTER  AND  EQUI- 
PARTITION  OF  ENERGY  IN  THE  NEWTONIAN  WORLD 

It  was  established  by  Dal  ton  and  his  contemporaries  that  mat- 
ter is  constituted  of  an  aggregate  of  discrete  entities  which  are 
all  alike  for  any  homogeneous  substance.  The  smallest  portion 
of  matter  that  can  be  manipulated  by  the  chemist  consists  of  a 
vast  assemblage  of  molecules,  and  his  knowledge  always  relates 
to  the  average  behavior  and  relations  of  a  crowd  of  molecules. 
Among  the  smallest  quantities  of  unelectrified  matter  ever 
detected  was  that  of  neon,  one  of  the  inert  gases  of  the  atmos- 
phere (there  is  about  one  part  of  neon  to  100,000  parts  of  air). 
Prof.  Strutt  has  shown  that  the  neon  in  one-twentieth  of  a  cubic 
centimeter  of  air  at  ordinary  pressure  could  be  detected.  In  this 
quantity  of  air  there  are  about  ten  million  million  molecules  of 
neon,  or  seven  million  times  as  many  neon  molecules  as  there 
are  people  in  the  world. 

Dealing  thus  with  such  immense  numbers  of  molecules,  it  is 
not  surprising  that  nothing  concerning  any  possible  individu- 
ality of  atoms  and  molecules  has  ever  been  detected.  Indeed, 
little  is  known  of  the  nature  of  neutral  atoms  and  molecules,  or  of 
the  forces  that  operate  in  interatomic  spaces.  All  our  laws  are 
for  masses  of  matter  that  are  extremely  large  compared  with 
atoms,  and  cannot  be  applied  to  'them,  without  exterpolation. 
However,  chemists  have  shown  that  all  matter  is  made  up  of  a 
number  of  elementary  substances  which  they  cannot  decompose. 
The  relative  weight  of  the  atoms  of  these  elements  are  known,  and 
it  is  becoming  more  and  more  probable  that  chemical  combina- 
tion consists  of  an  arrangement  of  atoms  alongside  of  each  other 
under  steady  cohesive  forces,  the  properties  of  each  atom  being 
somewhat,  though  not  essentially,  modified  by  the  near  presence 
of  the  others.  It  is  not  wonderful  then,  that  although  we  are 
certain  that  molecules  have  a  very  definite  structure,  when  we* 
inquire  into  the  details  of  their  constitution  we  do  not  have  much 
more  than  the  distant  analogy  of  familiar  dynamical  systems  to 
aid  us. 

43 


44  FUNDAMENTAL  PHYSICS 

The  last  century  gave  us  a  good  example  of  how  assumptions 
and  hypotheses  that  are  not  disproved  by  experiment  seem  to  us 
like  the  truth  itself.  The  analytical  methods  of  chemistry  suc- 
ceeded in  showing  that  all  matter  was  composed  of  some  ninety- 
two  elements.  As  no  division  of  matter  smaller  than  the  atom 
was  known,  and  as  no  case  was  known  of  the  loss  or  gain  of 
weight,  one  of  the  most  fundamental  properties  of  matter,  scien- 
tists in  general  began  to  consider  the  elementary  atoms  as  the 
foundation  stones  of  the  material  universe,  which,  amid  all  the 
changes  of  molecular  structure,  remained  forever  the  same. 

On  the  physical  side,  the  mathematical  development  of  the 
kinetic  theory  of  gases  has  extended  the  utility  of  the  atomic 
theory  very  greatly.  In  the  kinetic  theory  the  properties  of 
gases  are  explained  by  assuming  every  gas  to  be  composed  of 
minute  particles  or  molecules  in  continuous  motion,  colliding 
with  each  other  at  intervals  that  are  short  compared  with  the 
times  between  collisions.  No  definite  conception  of  the  mole- 
cules or  of  the  forces  acting  between  them  is  assumed.  The 
molecules  could  either  be  considered  to  be  elastic  spheres  or 
Boscovitch  centers  of  force,  and  the  gas  would  show  the  'same 
general  statistical  properties. 

The  kinetic  theory  of  gases  affirms  that  matter  is  composed  of 
definite  units  of  mass  or  molecules,  and  that  heat  energy  con- 
sists of  the  kinetic  energy  of  the  motion  of  these  molecules. 
This  kinetic  energy  may  consist  of  energy  of  rotation  as  well  as 
of  translation. 

In  1859  Maxwell  announced  the  theorem  of  the  partition  of 
kinetic  energy.  In  more  recent  years  the  mathematical  demon- 
stration has  been  perfected  by  Maxwell,  Boltzmann,  Jeans,  and 
others,  so  that  the  evidence  has  become  quite  strong  in  favor  of 
the  hypothesis  that  energy  is  distributed  equally  among  different 
types  of  molecules  and  also  among  the  various  degrees  of  freedom 
of  each  type  of  molecule  considered  independently.  The  mole- 
cules seem  to  be  surrounded  by  fields  of  force,  and  it  is  probably 
these  fields  that  we  measure.  Apparently,  collisions  take  place 
when  molecules  approach  each  other  sufficiently  close  for  their 
fields  of  force  to  slightly  overlap.  The  nature  of  these  forces  is 
such  that  molecules,  on  collision,  behave  like  elastic  spheres, 
practically  none  of  the  kinetic  energy  of  heat  being  frittered 
away  into  energy  having  a  comparatively  high  frequency. 

The  nature  of  molecular  forces  is  a  problem  concerning  which 


ATOMIC  STRUCTURE  OF  MATTER  45 

a  great  number  of  assumptions  have  been  made.  As  an  example 
we  may  take  a  few  hypotheses  as  applied  to  liquids.  Mills 
was  able  to  explain  some  latent  heat  phenomena  by  assuming  a 
molecular  attraction  obeying  the  inverse  square  law.  Klee- 
man  has  deduced  the  following  law, 


(I.  !\ 
\X.TJ 


where  Z  is  the  distance  between  the  molecules,  S  \/mi  is  the  sum  of 
the  square  roots  of  the  atomic  weights  of  the  atoms  of  the  mole- 
cule, Xc  is  the  distance  between  the  molecules  at  the  critical 
temperature,  Tc,  and  the  function  <p  is  unknown  though  it  is 
constant  at  corresponding  temperatures.  In  the  equation  of 
state  of  Van  der  Waals,  it  is  assumed  that  the  attraction  between 
molecules  varies  as  the  inverse  fourth  power  of  the  distance  be- 

K2 

tween  them.     Tyrer  gives  the  law  -^  where  K2  is   a   constant 

for  a  given  pair  of  molecules,  and  n  is  not  less  than  5  and  may  be 
greater  than  7. 

Fortunately  many  of  the  properties  of  gases  can  be  treated 
without  any  assumptions  being  made  as  to  the  nature  of  the  mole- 
cular forces,  the  molecules  being  considered  as  perfectly  elastic 
bodies  occupying  a  certain  volume  of  space,  and  possessing  a 
certain  amount  of  heat  energy. 

The  general  theorem  of  equipartition  of  energy  states  that  the 
energy  of  the  body  is  distributed  among  the  different  degrees  of 
freedom  by  which  the  state  of  the  body  as  a  dynamical  system  is 
described,  and  that  an  equal  share  is  allotted  to  each  degree  of 
freedom.  The  mathematical  development  contains  assumptions 
that  can  hardly  be  justified,  yet  experimental  evidence  corrobo- 
rates the  view  in  general. 

It  should  be  kept  in  mind,  however,  that  the  theorem  of  equi- 
partition must  be  applied  in  a  somewhat  restricted  form.  The 
energy  which  corresponds  to  certain  degrees  of  freedom  often 
does  pass  away  rapidly  as  energy  of  radiation,  whereas  the  en- 
ergy of  other  degrees  of  freedom  passes  away  with  extreme  slow- 
ness and  by  indirect  means.  It  is  the  latter  energy  that  is  indi- 
cated by  the  thermometer  and  is  distributed  equally  among  the 
degrees  of  freedom  of  this  type.  Jeans  assumes  that  the  de- 
grees of  freedom  that  permit  their  energy  to  be  lost  by  radiation 
also  possess  a  temperature  which  he  calls  subsidiary.  The 
two  types  of  degrees  of  freedom  are  called  principal  and  vibra- 


46  FUNDAMENTAL  PHYSICS 

tory.  When  a  gas  is  heated,  practically  all  the  energy  is  dis- 
tributed among  the  principal  degrees  of  freedom. 

The  distribution  of  energy  in  different  degrees  of  freedom  of  the 
molecules  of  various  gases  has  been  treated  in  popular  manner  by 
Magie  and  others,  and  serves  to  indicate  the  nature  of  molecular 
structure.  Let  Cv  be  the  specific  heat  of  a  gas  at  constant  vol- 
ume; Cp  the  specific  heat  at  constant  pressure;  E0  the  increase 
in  the  energy  of  translation  of  the  molecules  of  a  gas  when  the 
temperature  is  raised  from  0°  to  1°C.  at  constant  volume;  K 
the  energy  corresponding  to  one  degree  of  freedom  which  a  gram 
molecule  of  the  gas  receives  when  its  temperature  is  raised  1°C.; 
m  is  the  molecular  weight;  and  7  =  CP/CV.  From  the  laws  of 
thermodj^namics  it  follows  that 

2E0 

7  ~  l  =  3  Cv 

Assume  that  each  one  of  the  n  degrees  of  freedom  acquire  the 
same  amount  of  kinetic  energy,  say  K,  The  energy  of  transla- 
tion is  then  increased  by  3K,  so  that 


Where  P  is  an  unknown  quantity  of  potential  energy. 

Assuming  that  P  =  o,  and  that  the  molecules  are  points  having 
nothing  but  translational  energy,  n  =  3:  7  =  1.66.     This  value 
of  7  is  obtained  experimentally  for  the  monatomic  gases.     Fol- 
lowing is  given  a  table  of  valus  of  7  and  n  calculated  from  the 
2 

formula.  7  =  1  -\ j— 5- 

n  -\-  o 

Gas  7                      n 

Mercury 1.666  3.00 

Krypton 1.666  3.00 

Helium 1.652  3.07 

Neon 1.642  3.12 

Argon 1.63  3.20 


Ethylene 1.248  8.06 

Hydrogen 1 . 402  4 . 98 

Nitrogen 1.405  4.94 

CO 1.409  4.89 

Air 1.405  4.95 

Nitric  oxide 1.394  5.08 

Oxygen : 1.402  4.98 

CO2 1.300  6.67 

Nitrous  oxide ...  1 . 304  6 . 58 


ATOMIC  STRUCTURE  OF  MATTER          47 

Assume  that  P  is  due  to  the  displacement  of  the  atoms  in 
the  molecule.  Assume  that  the  motions  of  these  atoms  are 
simple  harmonic;  then  the  mean  value  of  P  corresponding  to 
each  internal  degree  of  freedom  is  equal  to  the  mean  kinetic 
energy.  Let  a  be  the  number  of  degrees  of  freedom  of  the  atom 
taken  as  a  whole,  and  i  the  number  of  internal  degrees  of  freedom. 
Then 


.  .  __ 

Each  internal  degree  of  freedom  contains  equal  amounts  of 
kinetic  and  potential  energy,  each  amount  of  energy  being  equal 
to  that  in  an  external  degree  of  freedom. 

In  the  case  of  the  monatomic  gases,  i  =  o,  n  =  3,  0  =  3 
mCp  =  4.943.  The  theoretical  value  of  7  is  1%,  and  it  is  found 
experimentally  that  the  value  of  7  ranges  between  1.64  and  1.66 
for  mercury  vapor,  krypton,  helium,  and  argon  and  the  vapors 
of  many  metals.  The  value  of  7  therefore  indicates  that  the 
whole  energy  of  these  gases  is  translational,  and  that  the  mole- 
cules of  these  gases  are  spherically  symmetrical  so  far  as  their 
internal  structure  is  concerned.  If  the  structure  of  the  molecules 
was  not  spherical,  some  translational  energy  would  be  changed 
into  rotational  energy  at  each  collision,  but  the  value  of  7  indi- 
cates that  there  is  no  such  equipartition,  and  the  dissipation  of 
this  rotational  energy  must  be  very  small,  since  the  gas  loses 
energy  very  slowly.  It  therefore  follows  that  little  if  any  energy 
goes  into  producing  rotation. 

In  the  case  of  diatomic  molecules,  the  value  of  n  =  5  gives  a 
value  of  7  that  agrees  very  well  with  the  experimental  value  as 
found  for  hydrogen,  nitrogen,  oxygen,  nitrous  oxide  and  hydro- 
bromic  acid.  This  value  of  n  corresponds  to  the  number  of 
external  degrees  of  freedom  if  the  distance  between  the  atoms  of 
these  molecules  remains  constant.  The  values  of  7  for  chlorine, 
bromine  and  iodine,  indicate  that  each  of  these  gases  has  an  in- 
ternal degree  of  freedom  to  which  energy  is  distributed. 

The  possibility  of  the  variability  of  the  distance  between  the 
atoms  of  some  of  the  diatomic  molecules,  may  be  correlated 
with  the  fact  that  bromine,  iodine  and  chlorine  have  such  char- 
acteristic absorption  spectra,  and  dissociate  at  comparatively 
low  temperatures. 


48  FUNDAMENTAL  PHYSICS 

The  elucidation  of  the  conditions  underlying  the  partition  of 
energy  among  the  degrees  of  freedom  of  bodies  is  a  very  inter- 
esting and  important  study  and  the  few  data  here  given  serve 
more  as  an  illustration  of  the  subject  than  as  an  outline  of  our 
knowledge. 


12.  THE  DISINTEGRATION  OF  ATOMS  BY  RADIO- 
ACTIVITY AND  THE  NATURE  OF  OUR  SYSTEM 
OF  MATTER  ELEMENTS 

Some  very  remarkable  relationships  have  been  discovered  in 
recent  years  as  regards  the  nature  of  the  system  of  matter  atoms. 
Atoms  have  been  compared  as  regards  their  atomic  weights, 
their  chemical  properties,  their  electrical  properties,  their  spectra 
and  lastly  and  probably  most  fundamentally  by  means  of  their 
characteristic  x  radiations,  as  discovered  by  Moseley,  and  which 
states  that  the  square  root  of  an  atom's  x  radiation  frequency 
is  proportional  to  the  atomic  number  which  represents  the 
number  of  excess  electrons  outside  the  nuclei.  This  law  gives 
92  elements  all  but  six  of  which  have  been  discovered. 

The  disintegration  of  the  atoms  of  uranium  and  thorium  into 
a  large  number  of  resultant  atoms  in  a  genetic  series  has  thrown 
much  light  upon  the  nature  and  the  relationships  of  the  high- 
number  atoms  and  that  these  atoms  all  contain  helium.  The 
discovery  that  an  atom  of  lead  may  have  a  variable  atomic 
weight  and  yet  manifest  the  same  chemical  properties  and  emit 
the  same  spectral  lines  has  lead  to  the  theory  of  isotropes,  atoms 
that  we  ordinarily  consider  alike  as  regards  their  properties 
except  as  regards  the  exact  nature  of  their  nucleus  and  which 
have  different  disintegration  histories. 

The  law  governing  the  rate  of  disintegration  of  any  simple 
radioactive  element  or  product  is  an  exponential  one.  If  there 
are  N0  atoms  of  this  product  at  a  time  t  =  0  and  N  atoms  at  the 
time  t  then, 

N  =  Ntf-" 

e  is  the  base  of  the  natural  system  of  logarithms  and  X  is  a  con- 
stant characteristic  of  the  given  radioactive  substance.     One 

has, 

(IN  - xt 

^i  =  -  7V0  Xe         =  -  \N 
at 

The  number  of  atoms  disintegrating  per  second  is  a  fraction 
equal  to  the  product  of  X  and  the  number  of  atoms  existing  at 
4  49 


50  FUNDAMENTAL  PHYSICS 

the  time.  The  same  law  applies  to  an  irreversible  monomolecular 
chemical  reaction.  The  time  (71)  required  for  half  the  active 
material  to  disintegrate  is 

#_  =  1  =     ~xr      T  =  log  2 
No      2  Xloge' 

The  average  life  of  any  atom  0  is  given  as  follows: 

—  ^  <  X  N  dt  =  —  I     \  N  t  dt  =  —  I     Note~™=~  =  0 

The  disintegration  of  a  mixture  of  radioactive  substance  can 
be  obtained  in  the  same  way  as  given  above,  the  computations 
becoming  quite  difficult  however,  for  a  large  number  of  radio- 
active substances. 

The  above  law  for  the  disintegration  of  a  simple  radioactive 
substance  is  that  given  by  chance.  Let  \dt  be  the  probability 
that  an  atom  is  destroyed  in  the  time  dt.  If  this  probability 
is  independent  of  the  instant  considered  and  of  the  number  of 
atoms,  then  X  is  a  constant.  If  N  is  the  number  of  atoms  and 
—  dN  the  number  that  disintegrate  in  the  time  dt,  one  has, 

-~=\dtaudN  =  JVoe"X<. 

This  law  only  applies  when  N  is  very  large.  When  N  is  small 
the  value  of  -dN  will  show  fluctuations  with  the  time. 

There  appears  to  be  a  relation  between  the  velocity  of  the 
emitted  a  particle  and  the  constant  of  disintegration  X.  A 
form  of  this  relation  sometimes  given  is  log  X  =  a  +  bVn,  a  and 
6  being  constants,  V  the  initial  velocity  of  the  a  particle  and  n 
a  number  such  as  1  or  2.  The  complexity  of  ft  rays  and  the 
possible  diffraction  effects  produced  by  7  rays  promises  to  give 
us  many  valuable  glimpses  into  disintegration  phenomena. 

In  the  radioactive  changes  that  take  place  with  the  emission 
of  ft  rays,  the  ft  particles  may  be  ejected  from  the  atom  through 
different  "avenues."  The  emission  of  7  rays  may  therefore, 
depen^l  upon  the  "avenue"  through  which  the  ft  particle  escaped. 
According  to  Rutherford  it  seems  that  7  rays  are  the 
"characteristic"  x  radiation  of  the  given  element.  Rutherford 
has  also  shown  that  the  energy  of  the  ft  particles  emitted  by  a 
product  such  as  radium  C  can  be  represented  by  a  value  pEi  + 
qEz  where  E\  and  E2  are  constants  and  p  and  q  are  positive 


THE  DISINTEGRATION  OF  ATOMS  51 

integers  (or  zero)  having  a  different  value  for  each  group  of  /3 
rays.  A  detailed  energy  study  of  the  radiations  will  throw 
much  light  on  radiation  theory. 

The  nature  of  molecular  collision  phenomena  indicates  that 
the  outer  regions  of  the  molecules  and  atoms  are  the  seats  of 
repulsive  forces.  Whether  the  atoms  possess  a  structure  or 
"shell"  from  which  certain  "avenues"  of  egress  or  absorption 
of  electrons  is  possible  is  of  course  an  open  question.  If  as  we 
believe  there  are  reasons  for  assuming  a  structure  for  the  ether 
in  the  nature  of  a  lattice  work  it  is  natural  to  expect  the  atonis 
to  possess  a  peculiar  ether  framework.  In  the  ether  vortex 
theory  the  atom  contained  closed  vortex  rings.  We  may  pic- 
ture the  atoms  as  containing  closed  ether  "threads"  or  "lines" 
of  force  such  that  an  electron  would  rotate  about  one  of  these 
closed  "lines"  of  force  in  the  same  way  that  it  follows  a  "line" 
in  the  ether.  The  repulsion  experienced  during  coPisions  would 
be  due  to  the  mutual  reactions  between  these  lines.  While 
following  a  "line"  the  electron  would  be  in  a  steady  state  but 
in  passing  to  another  line  radiation  might  take  place.  Isotropes 
such  as  radium  lead,  thorium  lead  and  ordinary  lead  might  pos-. 
sess  the  same  "line"  structure  and  would  be  alike  as  regards 
radiation  properties  while  the  nuclei  differ. 

Experimental  evidence  has  been  obtained  for  the  formation 
of  a  branch  series  in  the  study  of  radium  C.  Recoil  methods 
indicate  that  radium  C  is  complex  consisting  of  radium  Ci  and 
radium  (72.  A  very  small  amount  of  radium  Cz  is  obtained  by 
recoil  from  the  active  deposit  and  it  appears  that  radium  C\  may 
disintegrate  into  either  radium  D  or  radium  C2.  Similarly  in  the 
breaking  down  of  uranium  it  seems  that  two  products,  uranium 
X  and  uranium  Y  may  be  formed  simultaneously,  the  relative 
amount  of  uranium  Y  being  very  small.  In  the  case  of  thorium 
some  experimenters  have  concluded  that  thorium  C\,  and  the 
parent  of  thorium  Cz  are  simultaneous  products  of  thorium  B. 

K.  Fajans  considers  that  the  scheme  of  disintegration  of  RaB 
may  be  as  follows: 

RaC2  -*-» 

ft 
RaB  -»  RaC 


RaC'  7T^  RaD  -*  RaE  -»  RaF 


52 


FUNDAMENTAL  PHYSICS 


The  period  of  RaCi,  is  19.5  min.  and  of  RaCz,  1.4  min.  The  ra- 
tio of  the  numbr  of  atoms  disintegrating  in  the  branches  RaC2 
and  RaD  are  as  3  to  10,000  about. 


Atomic  Element  Uranium  series        Actinium  Series  Thorium  Series 

Number 


92         Uranium 

91         Uranium  Xi 

90        Thorium  loniui 

89        Actinium 

1 

88        Radium    ^  Radium 


uz 
^ 

UY 


UXi        RaAc 


Thorium       Radiothorium 


Niton 


i 
Nitor 


V      i. 
Actinium 


Mesothorium 


Act  niumX  Mesothorium    Thorium  X 


I  | 

Actinium  emanation  Thorium  emanation 


1  I 

84        Polonium    Radium  A       RaC'       RaF       Act.  A 


AcC' 


83        Bismuth 


82        Lead 


81         Thallium 


RaC 


RaB 


RaE 


I' 
RaD 


AcC 


Act  B 


lead 


lead 
RaC2 


ThC' 

k 


I 
lead 


lead 


lead 
lead 


I 
ThA 


1 
ThB 


ThD 


The  short  heavy  arrows  indicate  a  disintegration  where  a  /3 
particle  has  been  emitted  from  the  central  nucleus.  The  atomic 
number  is  increased  by  one.  A  long  arrow  indicates  the  loss  of 
an  a  particle  and  a  decrease  of  the  atomic  number  by  two.  Ele- 
ments with  the  same  atomic  number  are  isotropes  and  possess  the 
same  chemical  and  physical  properties.  Element  92  has  6 
valency  and  86  other  "outer"  electrons;  90  has  4  and  86;  88 
has  2  and  86;  86  has  0  and  86;  84  has  6  and  78;  82  has  4 
and  78. 


THE  DISINTEGRATION  OF  ATOMS  53 

The  radioactive  changes  of  the  atoms  are  of  tremendously  great 
value  in  analyzing  the  system  of  elements.  A  careful  comparison 
of  the  radiation,  atomic  weight,  chemical  and  other  properties 
of  the  atoms  leads  to  many  important  relationships  and  it  is 
not  being  too  optimistic  to  say  that  in  the  immediate  future  we 
may  discover  the  ultimate  elements  that  go  to  make  the  nuclei 
of  the  atoms  and  to  construct  the  family  tree  of  the  whole  sys- 
tem of  elements  and  to  learn  the  laws  involved  in  these  changes. 
Perchance  we  may  even  be  able  to  direct  some  of  these  changes. 


13.  ATOM  MODELS  AND  ATOM  NUCLEI 

Hypotheses  concerning  the  structure  of  atoms  are  compara- 
tively new  since  it  has  only  been  a  few  years  that  any  clues  have 
been  obtained  relating  to  inner  atomic  phenomena.  Lord  Kel- 
vin and  Helmholtz  were  inclined  to  view  atoms  as  a  type  of  vor- 
tex ring  in  the  ether  and  by  assuming  that  the  ether  was  a  fric- 
tionless  fluid  they  could  show  that  these  rings  would  continue  to 
rotate  forever  once  they  had  been  set  into  motion.  The  inde- 
structibility of  the  ether  atom  agreed  with  the  chemist's  views  at 
that  time.  Atomic  models  of  this  type  were  not  found  to  be 
helpful  in  "explaining"  the  properties  of  atoms  and  hence  they 
gradually  ceased  to  interest  investigators. 

The  discovery  of  the  electron,  the  prediction  of  the  effect  of  a 
magnetic  field  upon  the  vibrations  of  light  centers  by  Lorentz 
and  its  experimental  verification  by  Zeeman,  the  many  electron 
phenomena  of  spectroscopy  and  radioactivity,  the  Stark  effect 
of  an  electrostatic  field  upon  the  vibrations  of  light  centers,  the 
absorption  of  a  and  /3  rays,  Barkla's  and  Moseley's  work  on  x 
radiations,  these  and  many  other  phenomena  have  recently 
contributed  important  data  that  aid  greatly  in  an  interpretation 
of  the  intra-atomic  world  and  have  actually  made  the  subject 
of  atomic  structure  a  branch  of  experimental  science.  Inves- 
tigators have  therefore  frequently  endeavored  to  picture  the 
atomic  structure  from  their  point  of  view  as  being  spectroscopic, 
chemical  and  radioactive.  It  is  for  this  reason  that  the  same 
problem  has  been  elaborated  in  such  a  way  as  to  lead  one  to 
suppose  that  several  atom  models  are  equally  capable  of  explain- 
ing known  phenomenon.  In  the  present  chapters  we  will  de- 
scribe several  types  of  models. 

In  attempting  to  explain  atomic  structure  and  the  phenomena 
that  take  place  within  atoms  or  even  in  their  near  vicinity  we 
must  remember  that  we  have  truly  entered  into  a  mystic  "coun- 
try." Gravitation,  the  existence  of  point  forces,  our  laws  of 
mechanics,  of  magnetism  and  electrostatics,  our  methods  of 
measurement,  the  use  of  Euclidean  geometry,  the  nature  of 
light  and  electromagnetic  waves  may  be  meaningless  expressions 

54 


ATOM  MODELS  AND  ATOM  NUCLEI  55 

for  these  phenomena.  How  can  we  define  a  unit  of  length  to  an 
intra-atomic  being?  How  can  we  define  a  unit  of  time?  What 
is  the  nature  of  radiation  under  these  conditions?  Can  it  be 
expressed  by  equations  in  the  same  way  that  it  is  expressed  for 
free  space  or  are  its  properties  all  different?  What  happens  when 
a  beam  of  x-rays  pass  an  atom?  How  does  an  atom  absorb 
or  radiate  energy?  What  effect  does  a  violent  collision  have 
upon  an  atom?  What  takes  place  when  one  radioactive  atom 
changes  over  into  an  entirely  different  kind  of  atom? 

Amongst  the  earliest  types  of  the  electron  model  of  the  atom 
is  that  elaborated  by  J.  J.  Thomson.  This  atom  consisted 
of  a  uniformly  distributed  volume  charge  of  positive  electricity 
in  a  sphere  of  atomic  size.  In  the  outer  region  of  this  sphere 
were  large  numbers  of  negative  electrons,  the  charge  of  the  elec- 
trons being  equal  to  that  of  the  positive  sphere,  these  charges 
practically  neutralizing  each  other.  The  electrons  were  usually 
assumed  to  be  rotating  about  the  atom  in  much  the  same  way 
as  the  particles  in  the  rings  of  Saturn.  For  this  reason  Thom- 
son's atom  model  is  often  called  the  Saturnian  atom.  At  one 
time  it  was  thought  that  a  large  part  of  the  mass  of  this  atom  was 
due  to  the  electrons  in  it.  This  large  number  of  electrons  thus 
required  was  a  view  welcomed  by  the  spectroscopists  who  aim 
to  explain  the  complex  spectra  of  the  elements. 

The  Rutherford  atom  differs  from  the  Thomson  atom  in 
that  the  positive  charge  is  concentrated  into  a  small  volume  at 
the  center  of  the  atom.  Both  types  of  atom  assume  much  the 
same  distribution  of  negative  electrons.  The  Ritz  atom  model 
assumes  the  existence  of  magnetic  poles  and  makes  little  if  any 
use  of  positive  and  negative  charges  though  of  course  magnetic 
poles  could  be  obtained  by  the  proper  motion  of  one  or  more 
electrons.  A  free  magnetic  pole  (magneton)  has  also  been  as- 
sumed, the  magneton  playing  the  same  role  in  magnetic  phe- 
nomena that  the  electron  does  in  electricity.  Various  "dipoles" 
"neutrons,"  positive  electrons,  etc.,  have  been  hypotheticated. 

The  English  physicists  have  been  very  active  in  developing 
an  atom  model  for  the  interpretation  of  physical  phenomena 
and  probably  the  two  best  known  models  are  those  of  Thomson, 
and  Rutherford  and  Bohr.  The  early  work  of  Thomson  and 
others  of  the  Cambridge  school  proved  the  existence  of  elec- 
trons in  the  numerous  types  of  vacuum  tube  discharge,  in  the 
emission  of  electricity  by  hot  bodies,  in  the  photoelectric  effect 


56  FUNDAMENTAL  PHYSICS 

and  directly  or  indirectly  in  nearly  all  phenomena  of  ionization 
and  radioactivity.  The  Zeeman  effect,  dispersion  and  many 
other  optical  phenomena,  metallic  conduction  and  the  various 
electrical  and  thermal  properties  of  the  metals  indicated  that  the 
negative  electron  existed  as  a  component  part  of  practically 
every  kind  of  atom.  On  the  other  hand  no  corresponding  free 
"positive  electron"  has  ever  been  isolated  and  although  in- 
direct (spectroscopic)  evidence  of  its  existence  has  been  obtained 
yet  this  evidence  is  far  from  conclusive.  Positive  charges  are 
always  found  to  accompany  masses  of  atomic  size  so  that  it 
is  natural  to  assume  that  positive  charges  are  due  in  every  in- 
stance to  the  removal  of  negative  electrons  from  the  "atom." 
Positive  atom  ions  therefore  differ  amongst  themselves  in  the 
way  that  atoms  differ.  On  the  other  hand  negative  electrons 
appear  to  be  identical  no  matter  from  what  kind  of  atom  they  are 
removed. 

Thomson  naturally  assumed  his  atom  model  to  consist  of 
electrons  and  a  positive  charge  sufficiently  large  to'  neutralize 
the  charge  of  the  electrons.  The  positive  charge  was  consid- 
ered to  be  uniformly  distributed  throughout  the  atom,  the  elec- 
trons moving  about  freely  through  this  positive  charge  and  being 
attracted  toward  the  center  by  a  force  whose  intensity  is  indi- 
rectly proportional  to  the  square  of  the  distance  of  the  electron 
from  the  center.  Some  electrons  may  describe  closed  orbits 
within  the  atom  or  within  the  atom's  neighborhood  or  they  may 
vibrate  about  certain  positions  of  equilibrium.  Rings  of  electrons 
rotating  about  the  center  of  the  atom  may  exist.  These  rings 
may  all  be  in  one  plane  (Saturnian  atom)  or  they  may  be  located 
in  different  planes.  ' 

One  of  the  most  successful  simulations  of  the  Thomson  atom 
to  phenomena  is  its  "explanation"  of  the  various  families  of 
elements.  The  Mendelejeff  classification  of  the  elements  is 
based  largely  on  the  "valency"  properties  of  different  atoms  and 
Thomson  showed  how  a  model  containing  one  or  more  rings  of 
electrons  could  represent  the  different  families  and  the  different 
valencies.  The  analogy  is  indeed  very  striking  but  it  remains  a 
mere  analogy.  It  is  pretty  generally  conceded  that  valency 
in  chemistry  is  an  electron  phenomena  and  many  have  gone  so 
far  as  to  consider  the  valency  of  an  atom  to  be  the  number  of 
electrons  it  is  capable  of  gaining  or  losing.  This  view  of  valency 
gives  this  quantity  a  vector  quality.  This  interpretation  of 


ATOM  MODELS  AND  ATOM  NUCLEI  57 

valency  also  offers  a  picture  as  to  how  atoms  can  combine  with 
each  other  to  form  molecules  of  greater  or  less  stability.  Un- 
fortunately we  have  few  ways  of  verifying  any  conclusions  of  this 
kind  and  it  may  be  said  that  our  knowledge  of  interatomic  struc- 
ture is  more  certain  than  our  knowledge  of  intramolecular  struc- 
ture. On  the  whole  it  seems  quite  certain  that  chemical  phe- 
nomena and  most  of  the  physical  properties  of  substances  depend 
upon  "some  outer"  or  "valency"  electron  atmosphere  of  the 
atoms  and  that  the  remainder  of  the  atom  plays  a  very  small 
part  in  these  phenomena.  The  absorption  of  the  bullet  type  of 
radiation  (a,  /3  and  the  ion  radiations)  is  in  marked  contrast  to 
the  absorption  of  light  and  heat  and  is  more  or  less  entirely  in- 
dependent of  the  physical  and  chemical  nature  of  the  absorbing 
substance,  depending  only  upon  its  density.  According  to  this 
view  the  stability  of  atoms  is  to  be  attributed  to  the  part  other 
than  the  "electron"  atmosphere  while  the  wonderful  variety  of 
physical  and  chemical  changes  are  due  largely  to  the  changes 
taking  place  among  the  various  interlocking  electrons.  The 
universal  distribution  of  electrons  results  in  these  changes  being 
infinitely  more  simple  than  they  would  be  were  there  as  many 
types  of  electrons  as  there  are  atoms  of  matter.  The  im- 
penetrability of  solids  under  ordinary  conditions,  their  small 
diminution  of  volume  when  cooled  to  very  low  temperatures 
and  their  small  compressibility  seem  to  indicate  that  the 
"electron  atmosphere"  of  an  atom  or  molecule  possesses  quite 
a  definite  volume  which  is  not  greatly  affected  by  the  heat  mo- 
tions of  molecules. 

Some  interesting  models  of  the  Thomson  atom  have  been  made 
by  floating  magnets  upon  mercury  or  by  suspending  small  charged 
spheres  so  as  to  be  acted  upon  by  a  central  force.  Under  these 
conditions  the  magnets  and  spheres  arrange  themselves  in  con- 
centric circles  depending  upon  their  number  and  the  intensity 
and  direction  of  the  forces.  Probably  the  most  elaborate  work 
of  this  kind  has  been  done  by  Crehore.  By  assuming  definite 
models  it  is  possible  to  calculate  when  two  atoms  can  combine 
with  one  another  or  in  other  words  occupy  places  where  the 
interacting  forces  are  in  equilibrium.  These  positions  of  equilib- 
rium depend  upon  the  velocity  as  well  as  the  number  of  electrons 
in  the  model.  In  the  case  of  two  atoms  having  two  electrons  each 
it  is  shown  that  there  are  two  places  where  the  forces  of  attraction 
and  repulsion  neutralize.  In  this  way  it  may  be  possible  to 


58  FUNDAMENTAL  PHYSICS 

explain  the  size  of  molecules,  the  spheres  of  action  of  molecules, 
the  formation  of  aggregates,  etc. 

In  order  to  account  for  the  reflection  and  scattering  of  a  rays, 
Rutherford's  theory  assumes  that  the  atom  must  be  the  seat  of 
sufficiently  intense  electrical  forces  to  reflect  an  a  particle  in 
certain  encounters.  He  assumes  that  an  atom  possesses  a  central 
nucleus  of  charge  Ne  sufficient  to  neutralize  the  surrounding 
charges.  This  charge  is  considered  as  a  point  charge  and  an  a 
particle  passing  near  this  nucleus  will  be  caused  to  move  in  a 
hyperbolic  orbit  giving  a  deviation  <f>  to'the  a  particle,  where  Ne 
is  the  central  charge;  p  the  perpendicular  distance  from  the  nu- 
cleus to  the  original  path  of  the  a  particle,  E  the  charge  of  the  a 
particle  of  mass  m  and  velocity  v, 

2p 

- 


Let  a  beam  of  Q  a  particles  pass  through  a  thin  screen  of  thick- 
ness t  containing  n  atoms  per  unit  volume.  The  number  of  a 
particles  per  unit  area  (to  be  counted  by  the  scintillation  method) 
on  a  screen  at  a  distance  r  from  the  radiator  is 

ntb2  cosec4  ~ 
y  =      ~lQrr~ 
Geiger  has  found  that  y  varies  as  t ;  and  as  cosec4  ~  over  quite  a 

wide  range  of  angle.  The  value  of  Ne  is  about  lOOe  for  gold, 
N  varies  as  the  atomic  weight. 

Darwin  assumes  a  type  of  atom  similar  to  that  assumed  by 
Rutherford.  The  penetration  of  atoms  by  a  and  /3  particles  is 
then  reduced  largely  to  the  action  of  the  outer  electrons  in  re- 
ceiving energy.  Bohr  assumes  that  the  rate  of  decrease  of 
velocity  of  the  a  or  /3  particle  depends  on  the  frequency  of  vibra- 
tion of  the  electrons  in  the  absorbing  material.  Bohr  concludes 
that  the  hydrogen  atom  only  contains  one  electron  outside  the 
nucleus  while  the  helium  atom  contains  two  such  electrons. 

Nicholson  has  assumed  that  the  whole  mass  of  the  atom  is  of 
electrodynamic  form  due  to  the  presence  of  equivalent  amounts 
of  positive  and  negative  electricity.  The  negative  charge  con- 
sists of  electrons  and  is  now  generally  admitted  to  constitute  but 
a  small  part  of  the  total  mass  of  any  atom.  The  unknown  posi- 
tive charges  may  therefore  be  regarded  as  consisting  of  units  that 


ATOM  MODELS  AND  ATOM  NUCLEI  59 

are  very  small  compared  with  that  of  the  electron  and  since  the 

g2 

inertia  is  proportional  to  — *  e  being  the  charge  and  a  the  radius, 

the  mass  contributed  by  the  positive  charge  may  be  made  to 
represent  nearly  the  whole  atomic  mass.  These  positive  charges 
may  be  assumed  to  be  distributed  uniformly  throughout  the 
atom. 

The  single  positive  electron  is  not  supposed  to  exist  in  a  free 
state.  Permanence  may  be  assumed,  according  to  Nicholson, 
to  systems  of  two,  three,  four,  five,  etc.,  negative  electrons  in 
rings  at  equidistant  intervals  around  a  single  concentrated 
positive  charge.  Four  so-called  protyles  or  primary  atoms  are 
constructed  according  to  the  first  four  models  given  above  and 
the  atoms  of  the  various  elements  are  supposed  to  consist  of 
these  protyles  uniformly  distributed  throughout  their  volumes. 
These  protyles  are  coronuim,  hydrogen,  nebulium  and  proto- 
fluorine  respectively.  These  protyles  may  consist  of  multiples 
of  the  above  electron  construction.  Their  relative  atomic 
weights  are  Cu  0.5131;  H  1.008;  Nu  1.6277  and  Pf  2.3604. 
The  extraordinary  agreement  between  the  calculated  and  the 
observed  atomic  weight  is  remarkable. 

Element  Constitution      Calculated        International 

atomic  weight     atomic  weight 

Helium NuPf  3.988  3.99 

Lithium H2Nu3  6.900  6.94 

Glucinum H2Pf3  9.097  9.10 

Boron H3He2  11.000  11.00 

Carbon H4He2  12.008  12.00 

Nitrogen H6He2  14.020  14.01 

Oxygen H4He3  15.996  16.00 

Fluorine H7He3  19.020  19.00 

Neon H6Pf6  20.210  20.20 

Sodium H7He4  23.008  23.00 

Gold 8(He2Pf3H3)2(He2Nu2Pf3H3)Nu2Pf2H2 

Radium 8(He2Nu2Pf  3H3)2(He2Pf  3H3)He3. 

If  there  is  any  protyle  basis  of  the  theory  of  elements,  the 
disintegration  products  of  uranium  and  thorium  will  serve  as  a 
test  for  the  theory. 

A  few  characteristics  of  atomic  weights  as  considered  by 
Harkins  are : 

(a)  The  atomic  weights  on  the  hydrogen  basis  approximate 
whole  numbers  and  are  usually  lighter,  rather  than  heavier 


60  FUNDAMENTAL  PHYSICS 

than  the  nearest  whole  number.  Harkins  puts  forward  the 
theory  that  the  "packing"  of  hydrogen  atoms  in  the  nuclei  reduces 
their  mass. 

(6)  Since  the  alpha  particle  is  emitted  by  the  even  number 
elements  and  the  even  numbered  elements  of  low  values  show 
differences  in  their  atomic  weights  by  4,  there  is  evidence  that 
these  elements  are  helium  compounds,  nHe',  according  to 
Harkins. 

(c)  Most  of  the  odd  numbered  elements  of  low  atomic  weight 
can  be  represented  by  nHe'  +  H's,  the  primes  indicating  that 
the  mass  of  He  and  H  has  been  decreased  by  being  packed 
into  the  nucleus. 

(d)  Some  98  per  cent,  of  the  meteorites  consist  of  the  even 
numbered  elements.     As  far  as  abundance  of  the  elements  is 
concerned  the  system  plays  out  at  about  30.     The  conclusion  is 
reached  that  helium  forms  the  substructure  of  practically  all 
matter. 

The  Bohr  type  of  atom  is  quite  successful  in  explaining  the 
spectra  of  hydrogen  and  the  K  and  L  x  radiations  of  the 
elements.  The  following  items  briefly  indicate  the  nature  of 
the  model.  It  is  designed  for  radiation  purposes  and  is  con- 
sidered to  obey  the  classic  laws  of  electrodynamics  during  the 
steady  state.  It  is  during  this  steady  state  that  the  ordinary 
inverse  square  forces  are  assumed  to  hold. 

(a)  Assuming  that  the  inverse  square  law  holds  for  the  forces 
(F)  exerted  by  the  atomic  nucleus  (E)  upon  negative  electrons, 
then  Moseley's  law  leads  to  the  distance  (a)  of  the  innermost 
electron  (e)  orbit  from  the  nucleus  being  inversely  proportional 
to  the  atomic  number. 

F  =  —^  =  (27m)2  ma  or  for  two  different  atoms,  -\  =  -^rA 

(1  HZ 


with    Moseley's   law   yr  =  —  7=   one    has    -^r  =  —.     Millikan 

**«       Vw2  *»•       °2 

considers  that  these  conditions  can  be  assumed  because  only 
circular  orbits  are  to  be  considered  stable  and  are  indicated  by 
the  Zeeman  and  magnetic  effects. 

(6)  The  L  x  radiations  obey  Moseley's  law  in  the  same  way 
as  the  K  lines,  the  frequency  being  about  one-eighth  as  great. 
The  L  lines  indicate  the  second  electronic  orbit  to  be  about  five 
times  as  great  as  the  first. 


ATOM  MODELS  AND  ATOM  NUCLEI  61 

The  data  indicate  that  for  hydrogen  the  K  lines  appear  in  the 
ultraviolet  at  about  90/zM  as  has  been  obtained  by  Lyman. 
The  L  series  appears  to  be  the  ordinary  Balmer  series  in  the 
visible  spectrum.  The  M  series  is  Paschen's  infra-red  spectrum. 

(c)  The  frequencies  of  the  Balmer  series  of  hydrogen  is  given 

by  v  =  N  (^-j j-J  where   n\  =  2  in  the  visible  region  and 

n2  takes  values  3,  4,  5,  etc.,  for  the  different  lines.  Paschen's 
infra-red  lines  have  n\  =  3  and  Lyman's  bands  n\  =  1.  Bohr 
assumed  that  hydrogen  consisted  of  one  electron  rotating  about 
the  nucleus  in  a  series  of  nonradiating  orbits  governed  by 
conditions  described  in  (a). 

(d)  Radiation  takes  place  when  an  electron  moves  from  one 
orbit   (Ai)  to  another  (A 2)  in  such  a  way  that  hv  =  A\  —  A2 
where  h  is  Planck's  constant  and  AI  is  the  energy  of  orbit  1. 

(e)  The  possible  orbits  of  hydrogen  are  determined  by  the 
kinetic  energy  of  rotation   (T)  being  equal  to  %  rhn  where  r 
is  a  whole  number  and  n  is  the  orbital  frequency.     From  (c), 

(d)  and  (e)  N  =  T^ The  value  of  N  observed  spectro- 

scopically   agrees   with   that   calculated   for   this   Bohr   atom, 

.V  =  3.294(10) 15. 

/  jT2/i2  \ 

The  radii  (a  =  T — ^ — J  for  hydrogen  are  in  the  ratios  1,  4,  9, 

16,  25.  The  diameter  of  the  normal  hydrogen  atom  comes  to 
1.1  (10)~8  cm.  The  Bohr  atom  explains  why  hydrogen  does  not 
absorb  the  spectra  which  it  emits. 

(/)  Condition  (e)  implies  the  atomic  nature  of  angular 
momentum. 

(g)  The  smaller  the  number  of  electrons  in  the  outer  part 
of  the  atom  the  less  should  be  their  mutual  actions  and  hence 
the  less  deviation  from  the  Moseley  law.  This  is  found  to  be 
the  case. 

(h)  The  Bohr  view  of  the  atom  in  an  unmodified  form  applies  to 
hydrogen,  to  helium  that  has  lost  a  charge  and  to  the  inner 
electron  of  the  heavier  atoms.  The  fact  that  it  assumes  the 
electron  orbits  to  be  in  a  single  plane  does  not  necessarily  mean 
that  in  the  complex  atoms  a  disc  structure  is  necessary. 


14.    THE  RITZIAN   ATOM,  THE  MAGNETON   AND   THE 
NEUTRON 

Important  work  on  the  series  of  spectrum  lines  has  been  done 
by  -Kayser  and  Runge,  Rydberg  and  Ritz.  Ritz  has  developed 
a  theory  of  the  constitution  of  the  atom  that  explains  the  series 
distribution  of  spectrum  lines  based  on  a  magneton  (Bauer). 

The  different  formulas  of  spectral  series  may  be  said  to  be  an 
extension  of  Balmer's  equation  for  the  principle  lines  of  hydrogen. 
This  series  is  the  secondary  spectrum  which  is  obtained  in  vacuum 
tube  discharges.  The  formula  is: 

w2          1          rl         I 


N  is  a  constant  and  m  is  the  number  of  the  line  under  considera- 
tion of  wave  length  \m.  Pickering  has  observed  a  series  of 
supposedly  hydrogen  lines  in  f  Puppis  that  follows  the  law  : 


The  constant  N  is  the  same  as  in  Balmer's  formula;  m  has 
the  values  1,  2  .    .    .    .     The  series  has  not  been  obtained  in 
the  laboratory.     Kayser  and  Runge  have  represented  series  by 
equations  of  the  form 
J. 
X, 

The  series  are  primary  or  secondary  according  to  the  values 
of  the  constants  A,  B,  C.  Rydberg's  -formula  can  be  stated  as 
follows: 

^-  =  A  +  Bm~2  +  Cm~3- 

The  formula  of  Ritz  is,  N  being  a  constant  for  all  elements 
while  a,  b,  a'  and  br  differ  for  the  various  elements. 

J_       1 1 

N\  ~  I  b\ 2 ' 

62 


THE  RITZIAN  ATOM  63 

Most  physicists  have  applied  the  same  kind  of  differential 
equations  to  the  source  of  light  vibrations  as  would  apply  to 
elastic  vibrations.  These  equations  contain  the  frequencies 
as  squares  while  the  simple  laws  of  series  lines  contain  the 
frequencies  as  a  first  power.  Ritz  assumes  that  the  frequency  of 
the  oscillations  is  proportional  to  the  force  that  produces  the 
oscillations,  the  force  being  due  to  a  magnetic  field.  The  inten- 
sity of  magnetic  field  required  is  about  (10)  8  gauss.  This  is  in 
agreement  with  the  theories  of  magnetism  of  Langevin  and 
Weiss  and  of  the  pressure  shift  of  Humphreys  and  Mohler, 
these  theories  assuming  a  field  of  about  (10)7  gauss. 

The  intense  magnetic  fields,  to  which  is  due  the  vibrations 
which  give  rise  to  series  lines,  consists  of  magnetic  poles  dis- 
tributed within  the  atom  according  to  simple  geometrical  laws. 
From  the  poles  come  fields  H  and  H'..  The  fields  Hn  and  H'n 
normal  to  the  plane  of  vibration  of  each  particle  determine  the 
frequency  of  its  circular  motion.  Increasing  the  intensity  of 
the  field  causes  a  proportionate  increase  in  the  frequency. 
Every  solid  of  revolution  rotating  around  its  axis  may,  by  a 
suitable  distribution  of  electric  charge,  become  equivalent  to 
a  linear  magnet.  When  the  magnetic  poles  approach  the  surface, 
the  electric  density  increases  indefinitely  in  their  vicinity  and 
the  surfaces  carrying  the  electricity  become  practically  equivalent 
to  point  charges.  These  solids  are  alternately  positive  and 
negative,  having  rotations  in  opposite  senses.  Electrostatic 
attraction  fixes  them  together  as  a  linear  chain. 

Ritz  supposes  that  the  magnetic  fields  within  atoms  is  due  to 
elementary  magnets  of  length  a  and  having  poles  of  intensity  m. 
According  to  this  view,  where  A  depends  on  the  charge  and 
mass  of  the  corpuscle, 


^»/J_          J_\. 

a2   \w2      m2/ 


which  is  the  same  equation  as  Balmer's.  To  explain  other  series 
it  is  assumed  that  the  orientation  of  the  magnets  with  respect 
to  the  corpuscle,  or  the  number  of  magnets  is  changed.  If  n, 
is  the  distance  of  the  electron  P  to  one  pole  N  and  n2  the  distance 
to  the  other  pole,  the  frequency  n  of  the  resulting  circular  vibra- 

tion is  :  n  =  HK  =  K/JL  (  —  ^  --  ^  }  •  By  letting  the  first  magnet 
have  a  length  ~,  one  obtains  Balmer's  formula.  Other  formulae 


64  FUNDAMENTAL  PHYSICS 

can  be  obtained  by  giving  different  values  to  n,  and  to  the  lengths 
of  the  magnet. 

The  theories  of  Ritz  also  explain  many  complicated  cases  of 
the  Zeeman  effect  and  Cotton  has  discussed  the  positive  Zeeman 
effect  in  terms  of  Ritz's  views  of  the  atom. 

According  to  Ritz  a  vibration  of  frequency  v  =  N  (-r J  is 

\TC          7YI  I 

produced  by  the  magnetic  field  of  (m  —  2)  elementary  magnets 
turned  toward  each  other,  which  are  all  identical:  in  addition  to 
this  magnet  series  the  electron  is  subject  to  rigid  combinations. 
Higher  numbers  of  the  order  correspond  to  higher  magnet 
polymerizations,  which  constantly  become  less  stable,  so  that 
the  lines  become  broader  with  an  increasing  number  of  the  order, 
and  also  become  constantly  weaker.  The  magnetic  field  in  an 
atom  Ritz  considers  as  being  produced  by  two  poles  of  opposite 
sign,  which  separately  may  occupy  different  positions  in  the 
atom.  In  the  case  of  hydrogen,  these  points  lie  at  equal  dis- 
tances on  a  straight  line.  In  any  combination  formula  each  of 
the  terms  represents  the  influence  of  one  pole,  and  the  possible 
positions  of  the  separate  poles  permit  the  most  varied  combina- 
tions of  the  poles  in  pairs.  As  to  a  certain  minimum  prescribed 
in  the  number  of  the  order  m — which  occurs  in  the  case  of  no 
known  processes  of  vibration — this  mode  of  representation  only 
affirms  that  the  magnet  poles  are  held  by  the  structure  of  the 
atom  at  a  certain  minimum  distance  from  the  electron  vibrating 
within  an  atom. 

The  theories  of  Ritz  have  been  applied  with  greatest  success 
to  series  spectra.  Band  spectra  may  be  considered  as  due  to 
closed  rings  or  polygons  of  elementary  magnets,  these  structures 
forming  an  important  part  of  the  atom.  A  series  spectrum 
may  result  when  these  structures  have  been  excited  in  some  way 
by  electrical  or  chemical  processes. 

The  researches  of  P.  Curie  and  others  showed  that  the  dia- 
magnetic  susceptibility  of  a  substance  is  independent  of  the 
temperature  whereas  the  paramagnetic  susceptibility  is  in- 
versely proportional  to  the  absolute  temperature.  Accordingly 
there  must  be  a  fundamental  difference  between  the  two  kinds 
of  magnetism.  Langevin's  theory  makes  diamagnetism  a  char- 
acteristic property  of  each  molecule,  the  resultant  magnetic 
moment  of  the  revolving  electrons  in  each  atom  being  zero. 
An  external  magnetic  field  only  affects  the  orbits  When  the 


K  X  (10)6 

K  X  (10)6 

Pb  -   1.37 

Cd. 

-1.16 

Au..,  -  3.07 

Tl., 

-4.6 

C,  diamond  —  0.49 

Cu. 

-0.82 

C,  amorphous  ....  —  2  .  02 

Al. 

1.8 

Hg  -  2.6 

Be 

0.29 

Ac...                   .  .  -   1.4 

R 

.     4.32 

THE  RITZIAN  ATOM  65 

revolving  electrons  possess  a  magnetic  moment  the  substance  is 
paramagnetic.     For  a  diamagnetic  substance  the  susceptibility 

K  =  2~  Nezrz,  m  being  the  mass,  e  the  charge  and  r  the  radius 

of  the  electron  orbits,  N  being   the  number  of  electrons  per 
unit  volume. 

K  x  (10)« 

Na 2.2 

Pd 5.15 

Pt 29.0 

Si 0.2 

N 0.0537 

Mo 2.2 

Bi -13.7         Mg 0.57        Os 0.62 

The  phenomena  of  magnetism  are  extremely  complex  and 
seem  to  be  very  closely  related  to  the  processes  that  take  place 
during  chemical  reactions,  in  optical  phenomena  and  in  mechan- 
ical changes.  These  properties  of  matter  appear  to  be  due  to 
electrons  revolving  in  orbits  in  the  outer  parts  of  atoms. 

According  to  Langevin  molecules  contain  a  large  number  of 
electrons  moving  in  closed  orbits,  each  of  which  has  a  certain 
magnetic  moment.  In  an  increasingly  intense  magnetic  field, 
according  to  Lenz's  law,  the  motion  of  the  electrons  would  be 
modified  so  as  to  oppose  the  increase  of  the  intensity  of  the  field 
and  would  thus  show  the  phenomena  of  diamagnetism,  as  well 
as  the  Zeeman  effect.  Paramagnetism  is  then  only  the  property 
of  such  molecules  or  aggregates  whose  resultant  magnetic 
moment  is  not  zero.  The  theory  of  Langevin  fails  to  explain 
many  of  the  magnetic  properties  of  solids  although  it  explains 
the  magnetic  properties  of  oxygen. 

In  order  to  explain  the  magnetic  properties  of  solids,  Weiss 
imagines  a  molecular  magnetic  field  that  is  to  be  measured  by  the 
magnetic  action  of  an  aggregate  of  molecules  upon  any  one  of 
them.  Such  a  field  is  considered  as  uniform  and  its  intensity 
and  direction  are  given  by  its  effect  on  the  hypothetical  isolated 
molecule.  If  Hm  is  the  strength  of  the  molecular  field,  d  the 
density  of  the  magnetic  material,  m  its  molecular  weight,  A  a 
constant  and  Om  the  magnetic  moment  per  gram-molecule  of 
material, 


66  FUNDAMENTAL  PHYSICS 

o-m0  is  the  limiting  value  of  <rm  when  H  becomes  very  large  or 
T  (the  absolute  temperature)  very  small  ;  a  =     p 


According  to  the  theory  of  Weiss,  the  magnetic  moments  of 
molecules  are  integral  multiples  of  a  common  magnetic  moment 
which  he  calls  the  magneton.  This  unit  magnetic  moment 
would  be  expected  to  be  independent  of  the  temperature,  the 
latter  affecting  the  size  and  arrangement  of  the  molecular 
aggregates. 

Weiss  and  Onnes  have  studied  the  magnetic  properties  of 
various  ferromagnetic  substances  at  low  temperatures  and  the 
following  gives  the  experimental  value  of  the  magnetic  moment 
of  a  gram  atom  or  of  a  ^  gram-molecule. 

Nickel  .................................  3,381 

Cobalt  .................................  9,650 

Iron  ...................................  12,410 

Magnetite  .............................  7,417 

The  values  for  iron  and  nickel  are  quite  exact  and  are  in  the  ratio 
of  11:3.  After  making  certain  temperature  corrections  Weiss 

calls  —  ^  —  =  —  »  —  =  1123.5,  the  gram  magneton.     Dividing 

by  the  number  of  atoms  in  a  gram-atom  Weiss  gets  a  number 
16.4  (10)~22  which  he  considers  to  be  the  magnetic  moment 
of  the  magneton  or  elementary  magnet.  A  magnetic  molecule 
is  a  quantity  of  matter  whose  magnetic  axis  possesses  2  degrees 
of  rotational  freedom. 


Substance  Zm(10)«  <rm0 

FerrocyanideofKandNH4 1.73  11.70  10.41 

Pyrophosphate  of  Fe  and  NH4 7 . 99  24 . 60  21 . 89 

Ferric  and  ammonium  citrate 8 . 04  24 . 68  21 . 96 

Sodium  ferripyrophosphate 9 . 66  27 . 10  24 . 04 

Sodium  ferrimetaphosphate 13 . 00  31 . 50  28 . 03 

Ferric  chloride 13.10  31.39  27.93 

Ferric  sulphate 15.20  33.80  30.09 

Potassium  f errometaphosphate 1 1 . 30  29 . 20  25 . 99 

Sodium  ferro-oxalate 12.30  30.48  27.11 

Sodium  ferropyrophosphate 13 . 00  31 . 37  27 . 91 

Ferrous  sulphate 12.90  31.12  27.69 

Uranium  sulphate 3.24  15.76  14.03 


THE  RITZIAN  ATOM  67 

The  Parson  "electron"  or  "magneton"  (Smith,  "Misc.  Col- 
lections," Vol.  65,  No.  11,  '  1915)  is  a  thin  ring  of  negative 
electricity  (about  1.5  (10)~9  cm.  in  radius)  revolving  with  a 
velocity  approaching  that  of  light  and  possesses  electrostatic 
and  magnetic  properties. 

The  change  of  wave  length  of  spectrum  lines  due  to  increase  of 
pressure  discovered  by  Humphreys  and  Mohler  has  been  attri- 
buted by  Humphreys  as  being  due  to  the  magnetic  properties 
of  surrounding  atoms.  This  theory  was  advanced  owing  to  a 
supposed  connection  with  the  Zeeman  effect.  Livens  attributes 
the  effect  to  an  increase  in  the  density  of  the  vapor  emitting  or 
absorbing  the  given  light. 

Duane  has  proposed  a  magnetic  moment  (M)  for  the  holding 
of  positive  nuclei  (E)  together  against  their  electrostatic  repulsion. 
He  proposes  to  account  for  the  ejection  of  an  a  particle  by  assum- 
ing that  it  is  disturbed  sufficiently  for  it  to  get  beyond  the  critical 

E2       QM2 
magnetic  field.     The  critical  distance  70  is  —5  =  — T-  and  if  the 

7*0  TO 

disturbed  displacement  exceeds  r0  the  a  particle  will  escape. 

Oxley  finds  that  the  change  of  magnetic  susceptibility  on  the 
crystallization  of  some  40  diamagnetic  substances  indicates 
fields  of  107  gauss.  Merritt  has  intimated  that  the  fluorescence 
of  uranium  compounds  gives  evidence  of  the  presence  of  magnetic 
fields. 

Some  experimenters  have  resorted  to  the  view  that  a  gas  may 
contain  certain  molecules,  or  neutrons,  which  are  in  a  condition 
allowing  of  easy  ionization.  Neutrons  may  themselves  be  formed 
by  the  action  of  ionizing  agents.  One  can  easily  imagine  a  di- 
atomic molecule  being  split  into  the  monatomic  condition,  and 
these  atoms  may  be  comparatively  easy  to  ionize.  According 
to  Wellisch  and  Bronson  a  rays  may  produce  neutrons, 
relatively  more  neutrons  being  formed  in  the  early  part  of  the 
range  of  the  a  particle.  In  this  way  an  effort  is  made  to  explain 
the  fact  that  the  "saturated"  portion  of  the  ionization, current 
curve  is  not  parallel  to  the  current  axis.  The  radioactive  rest- 
atoms  are  considered  to  be  in  the  neutron  condition. 


15.  THE  CORPUSCULAR  THEORY  OF  LIGHT 

The  nature  of  light  and  of  radiant  energy  in  general  has  been 
a  subject  of  discussion  ever  since  the  introduction  of  the  experi- 
mental method  in  science.  Among  the  classic  controversies  on 
this  subject  was  that  between  Newton,  Hooke  and  others  of 
the  time.  Hooke  supported  the  wave  theory  while  Newton 
upheld  the  view  that  light  consisted  of  the  propagation  of  some 
sort  of  corpuscular  radiation.  Hooke  believed  that  space  was 
permeated  by  an  elastic  medium,  the  ether,  which  was  capable 
of  propagating  vibrations.  This  ether  pervaded  matter  in  which 
it  possessed  less  density  than  in  free  space,  and  it  did  not  neces- 
sarily consist  of  a  single  substance. 

Newton  considered  that  ether  and  the  light  "emanation" 
were  capable  of  mutual  interaction  and  that  when  light  passes 
through  strata  of  ether  of  different  densities,  it  was  deflected 
from  its  rectilinear  course.  The  heat  resulting  from  the  ab- 
sorption of  light  Newton  thought  might  be  due  to  vibrations 
set  up  in  the  ether.  Color  was  associated  with  some  property 
of  the  corpuscles  acting  in  a  way  somewhat  like  Helmholtz 
resonators  in  setting  up  waves  in  the  surrounding  medium  of 
different  frequencies. 

It  may  be  of  interest  to  note  that  it  was  customary  for  chemists 
to  include  light  corpuscles  among  the  chemical  elements  for  a 
long  time  after  Newton  had  died.  When  Lavoisier  announced 
however,  that  the  weight  of  substances  was  the  same  before 
chemical  reactions  as  after  they  had  taken  place,  the  classifica- 
tion of  the  elements  became  much  the  same  as  that  used  today. 

About  this  time  radiant  heat  was  also  considered  to  consist 
of  rays-of  light-corpuscles.  When  it  was  found  that  light  and 
heat  could  be  separated  by  selective  absorption,  it  was  necessary 
to  accept  the  "heat  corpuscle"  as  a  separate  element  called 
caloric.  Caloric  was  considered  as  filling  the  interstices  be- 
tween the  particles  of  ponderable  matter.  This  view  gave  a 
reasonable  explanation  of  the  expansion  of  bodies  on  being 
heated.  Whether  caloric  possessed  weight  or  not  was  left  an 
open  question. 


16.  HUYGHENS'  SECONDARY  WAVELET  CENTERS 

To  explain  the  phenomena  of  color  Newton  assumed  that 
"every  ray  of  light,  in  its  passage  through  any  refracting  surface, 
is  put  into  a  certain  transient  constitution  of  state,  which,  in 
the  progress  of  the  ray,  returns  at  equal  intervals,  and  disposes 
the  ray,  at  every  return,  to  be  easily  transmitted  through  the 
next  refracting  surface,  and,  between  the  returns,  to  be  easily 
reflected  by  it."  The  "length  of  fit"  was  supposed  to  be  pro- 
portional to  what  we  now  consider  as  the  wavelength. 

At  about  the  same  time,  Huygens  wrote  his  defense  of  the 
wave  theory  of  light,  and  developed  the  principle  that  each 
surface  element  of  a  wave  front  or  locus  of  disturbance,  may  be 
considered  as  the  source  of  a  secondary  wave  which  will  be 
propagated  in  the  form  of  a  spherical  wave  if  the  medium  is 
isotropic.  The  wave  front  at  any  subsequent  time  is  simply  the 
envelope  of  the  secondary  waves  from  these  various  surface 
elements.  By  this  means  refraction  and  reflection  were  easily 
explained.  Huyghens  assumed  that  the  solid  particles  of 
transparent  bodies  affected  the  elasticity  of  the  ether,  and  thus 
altered  the  velocity  of  light  in  them.  Metals  were  opaque 
because  they  contained  the  particles  that  damped  the  luminous 
motion. 


17.  THE  FINITE  STRUCTURE  OF  THE  ELECTRIC  FIELD 

The  conceptions  of  Faraday  lead  naturally  to  the  view  that 
the  electric  and  magnetic  fields  may  possess  a  structure. 
The  electric  lines  of  force  may  occupy  only  a  small  portion  of  the 
space  which  they  traverse  and  a  finite  number  of  electric  lines 
of  force  may  radiate  outward  from  a  charge  of  given  value. 
Indeed  it  has  been  suggested  that  one  line  of  electric  force  might 
proceed  from  a  unit  charge  of  electricity  or  an  electroethon. 
The  cross  section  of  this  elementary  line  of  force  might  remain 
constant  or  it  might  vary  as  one  proceeded  away  from  the  electric 
charge  at  the  end  of  the  line.  In  other  words  the  electric  field 
might  be  considered  as  possessing  an  atomic  structure. 

The  conception  of  lines  of  magnetic  and  electric  force  is  very 
useful  in  discussing  a  large  number  of  physical  and  engineering 
problems.  For  these  purposes  any  arbitrary  unit  such  as  a 
Faraday  tube  of  electric  force  or  a  gauss  may  be  used. 

Light  may  be  pictured  as  a  transverse  motion  along  the  fibers 
of  the  ether.  The  energy  of  a  wave  front  would  not  be  distrib- 
uted uniformly  over  the  surface  but  would  be  concentrated  at 
the  points  of  the  surface  cut  by  the  lines  of  force. 

A  theory  of  this  kind  permits  considerable  latitude  of  varia- 
tion in  case  the  electric  charge  or  magnetic  pole  is  moving. 
Do  the  lines  of  force  move  with  the  charge  or  the  pole?  Do 
the  lines  of  force  consist  of  ether  threads  surrounded  by  vacuous 
space  or  do  they  consist  of  some  peculiar  state  of  the  ether? 
If  the  latter  is  the  case,  then  does  all  the  ether  move  with  the 
tubes,  or  part  of  the  ether  or  only  the  disturbance? 

When  lines  of  electric  force  cross  the  boundary  of  two  contigu- 
ous media  possessing  different  dielectric  constants,  the  necessary 
conditions  imposed  upon  the  differential  equations  representing 
the  electromagnetic  wave  motion  are  that  the  tangential  com- 
ponent of  E  on  either  side  of  the  boundary  is  continuous  and  the 
normal  component  of  the  electric  displacement  is  continuous. 

70 


FINITE  STRUCTURE  OF  THE  ELECTRIC  FIELD  71 

This  involves  a  refraction  of  the  line  of  force  in  crossing  the 
boundary.  If  the  dielectric  constants  (Ki  and  KZ),  the  angles 
which  the  lines  of  force  makes  with  the  normal  (0i  and  02),  the 
refractive  indices  for  light  (MI  and  /x2)  in  the  two  media  (1  and  2) 
are  given,  then : 

Ki  cot  61  =  Kz  cot  02  and  MI  sin  0i  =  ^2  sin  02. 

In  any  theory  of  the  transmission  or  reflection  of  electromag- 
netic waves  by  two  or  more  different  media  it  is  always  necessary 
to  make  certain  assumptions  concerning  the  boundary  conditions. 


18.  THE  ELECTROMAGNETIC   THEORY  OF  RADIA- 
TION, THE  THEORY  OF  GRAVITATION 
AND  THE  EQUIPARTITION  OF 
ENERGY 

Between  the  time  of  Newton  and  of  Faraday,  various  views 
were  taken  as  to  the  nature  of  electricity  and  the  medium  in  which 
electromagnetic  and  optical  phenomena  take  place.  During 
this  time  the  one  and  two  fluid  theories  of  electricity  were  in 
vogue.  After  the  establishment  of  the  wave  theory  of  light  by 
Young  and  Fresnel,  the  luminiferous  medium  was  treated  for  a 
long  time  as  an  elastic  solid.  No  connection  was  known  to  hold 
between  optical  and  electromagnetic  phenomena. 

It  is  to  the  genius  of  Faraday  that  we  owe  our  present  hypo- 
thetical working  models  as  to  the  structure  of  electrical  and 
magnetic  fields  and  the  correlation  of  electrical  and  magnetic 
phenomena.  The  curves  produced  by  sprinkling  iron  filings  on 
a  paper  placed  over  a  magnet  led  him  to  the  idea  of  magnetic 
lines  of  force,  curves  whose  direction  at  any  point  corresponds 
to  the  direction  of  the  magnetic  intensity  at  the  point.  Faraday 
considered  all  space  to  be  filled  with  these  magnetic  lines  of  force, 
every  line  being  a  closed  curve.  The  density  of  the  lines  of  force 
through  a  unit  area  is  taken  to  be  proportional  to  the  magnetic 
intensity  at  a  central  point  in  the  area,  and  its  magnitude  is 
arbitrarily  defined.  The  fundamental  principle  of  the  induction 
of  currents  was  discovered  by  Faraday  and,  stated  in  his  own 
words,  is:  "Whether  the  wire  moves  directly  or  obliquely  across 
the  lines  of  force,  in  one  direction  or  another,  it  sums  up  the 
amount  of  the  forces  represented  by  the  lines  it  has  crossed," 
so  that  "the  quantity  of  electricity  thrown  into  a  current  is 
directly  as  the  number  of  curves  intersected." 

Faraday  also  suggested  that  the  particles  of  an  insulating 
dielectric  under  the  action  of  an  electric  field  become  polarized, 
the  particles  acting  like  electrical  -doublets.  Lorentz  added  to 
the  theory  by  assuming  ions  to  exist  in  the  dielectric,  these  ions 
being  subjected  to  certain  elastic  and  viscous  forces. 

72 


ELECTROMAGNETIC  THEORY  OF  RADIATION  73 

We  may  consider  that  the  electromagnetic  theory  of  light  is 
due  to  Faraday,  for  it  was  he  who  suggested  that  if  the  existence 
of  a  luminiferous  ether  is  to  be  admitted,  it  may  also  be  taken  as 
the  seat  of  magnetic  phenomena  as  well. 

Maxwell  succeeded  in  translating  Faraday's  conceptions  into 
mathematical  equations.  The  lines  of  magnetic  or  electric  force 

represent  the  direction  of  a  vector  (B  =  \i.R  for  the  magnetic 

field  or  D  =  KE  for  the  electric  field),  and  the  magnitude  of  this 
vector  is  inversely  proportional  to  the  cross  section  of  the  tubes  of 
force  formed  by  the  lines.  This  relation  between  magnitude  and 
direction  is  a  property  of  any  circuital  vector  —  such  as  a  vector 
that  represents  the  velocity  of  an  incompressible  fluid  at  any 
point.  Hydrodynamical  sources  and  sinks  correspond  to  elec- 
trical charges  or  magnetic  poles. 

The  energy  of  electrification  resides  in  the  medium,  provided 
it  is  capable  of  transmitting  electrical  action. 

The  energy  in  any  part  of  the  medium  is  considered  by  Max- 
well to  exist  as  a  state  of  constraint  or  strain  called  the  electric 

polarization  (D  =  ^—  )•     In  general  the  direction  of  the  force 

(E}  and  the  displacement  are  the  same. 
The  energy  per  unit  volume  of  the  dielectric  arising  from  the 

polarization  is  ^ED  cos  6,  where  0  is  the  angle  between  E  and  D. 

In  "fluid"  dielectrics  the  electric  polarization  is  accompanied 
by  a  tension  in  the  direction  of  the  lines  of  force  equal  to  the  pres- 
sure in  all  directions  normal  to  the  lines  of  force,  the  amount  of 
the  tension  or  pressure  per  unit  area  being  numerically  equal  to 
the  energy  per  unit  volume  at  the  same  place. 

From  this  view  Maxwell  derived  his  equations  of  the  electro- 
magnetic field. 


=  kE 
B  =  nH 

4wD  =  kE     =  curl  H  . 
-  B  =  -  nH  =  curl  E. 


74  FUNDAMENTAL  PHYSICS 

The  entire  magnetic  intensity  round  the  boundary  of  any  surface 
measures  the  quantity  of  electric  current  which  passes  through 
that  surface. 

The  view  introduced  by  the  electromagnetic  theory  of  light  is 
that  the  energy  of  radiation  is  essentially  of  the  same  nature  as 
the  energy  that  is  localized  about  a  charged  body  either  at  rest 
or  in  motion.  The  ether  is  the  medium  of  the  energy  of  radiation 
and  of  electromagnetic  energy,  and  its  properties  are  so  chosen  as 
to  satisfy  the  requirements  of  the  equations  of  Maxwell.  As  far 
as  optical  phenomena  are  concerned  the  ether  medium  is  con- 
sidered homogenous  as  regards  its  power  of  containing  energy. 
The  velocity  of  radiation  is  rectilinear  and  is  the  same  in  every 
direction. 

In  his  "Thoughts  of  Ray  Vibrations"  Faraday  suggested  that 
an  atom  may  only  be  a  field  of  force  surrounding  a  point  center — 
a  view  similar  to  that  of  Boscovich  and  Michell.  Such  an  atom 
would  have  no  definite  size.  It  could  be  considered  as  completely 
penetrable  and  extending  throughout  all  space.  It  was  also 
suggested  that  light  and  radiant  heat  might  consist  of  transverse 
vibrations  propagated  along  the  lines  of  force  radiating  from  the 
atomic  centers.  In  this  way  Faraday  proposed  to  "dismiss  the 
ether." 

H.  A.  Lorentz,  in  1892,  began  a  series  of  memoirs  upon  an 
electron  theory — all  electrodynamical  phenomena  being  attri- 
buted to  moving  electric  charges.  In  contrast  to  the  older 
electron  theories  of  Weber,  Riemann  and  Clausius,  the  electrons 
were  considered  as  acting  upon  the  medium  rather  than  between 
each  other.  Electrons  do  not  (Clausius'  theory)  act  instan- 
taneously at  a  distance  but  through  a  space  subjected  to  Max- 
well's equations,  the  actions  being  propagated  with  the  velocity 
of  light. 

One  form  of  the  equations  of  Lorentz  is: 

div  D  =  47rc2p, 

div  H  =  0, 
curl  D  =  -  H 
curl  H  =  ^f>  +  47rpF 

The  "ponderomotive"  force  on  an  electron  of  charge  e  and 
velocity  V  being  eD  +  e[V-H]. 


ELECTROMAGNETIC  THEORY  OF  RADIATION  75 

The  equations  of  Lorentz,  based  on  the  electron  theory, 
assume  an  absolutely  motionless  ether  to  which  neither  density, 
elasticity  nor  any  mechanical  property  is  ascribed.  To  such  an 
ether  Thomson's  lines  of  force,  Lodges'  idea  of  density  and. 
Bjerknes'  and  Korn's  mechanical  analogies  would  have  to  give 
additional  properties. 

The  fact  that  radiant  energy  would  exert  a  definite  amount 
of  pressure  on  material  surfaces  was  first  predicted  by  Maxwell 
on  the  view  of  dielectric  stresses;  by  Bartoli  from  thermody- 
namic  principles  and  by  Planck  from  electrodynamical  prin- 
ciples by  assuming  a  perfect  reflector  to  be  a  perfect  electrical 
conductor.  The  electric  vector  of  a  light  beam  induces  a  finite 
charge  on  the  surface  of  the  reflector  and  a  finite  current  within. 
The  current  in  the  field  of  the  magnetic  vector  of  the  beam 
results  in  a  mechanical  force.  The  resultant  of  the  two  me- 
chanical forces  gives  the  radiation  pressure. 

If  R  represents  the  time  rate  per  unit  of  area  at  which  elec- 
tromagnetic energy  is  transferred  at  a  point  then  Poynting's 
theorem  gives  R  =  VEH  sin  6  where  6  is  the  angle  between  E 
and  H.  V  =  §Edr  along  a  line  of  electric  intensity.  By  using 
Poynting's  theorem  the  energy  of  the  electric  and  magnetic  fields 
is  ~E2  and  ~#2. 

O7T  O7T 

The  electromagnetic  theory  of  Maxwell  based  on  a  polarizable 
ether  and  the  mechanics  upon  which  it  rests  may  be  spoken  of  as 
the  classical  theory.  It  has  had  many  brilliant  successes  and 
from  it  many  of  our  laws  of  today  such  as  the  Rayleigh  law  for 
long  wave  length  radiation  and  the  Wien  displacement  law  for 
radiation  have  been  derived.  The  Rayleigh  law  assumes  the 
equipartition  of  energy  and  Wien  assumed  that  the  length  of  a 
wave  sent  out  by  a  molecule  depends  only  upon  the  velocity  of 
the  molecule  [V  =  /(X)]  and  the  intensity  of  the  radiation  be- 
tween X  and  X  +  d\  is  proportional  to  the  number  of  molecules 
(as  given  by  Maxwell's  law)  which  send  out  waves  between  X 
and  X  +  d\.  From  these  assumptions  the  intensity  of  radiation 
v(X,  9)d\  of  a  black  body  at  the  temperature  6  produced  by  the 
waves  X  to  X  +  d\  is 


6)  =  -&     where  C  and  c  are  constants. 


76  FUNDAMENTAL  PHYSICS 

The  principle  of  the  conservation  of  energy  asserts  that 
R  +  r  =  a  constant,  where  R  is  ordinary  mechanical  kinetic 
energy  and  r  is  the  "hidden  "  or  potential  energy.  If  the  system 
can  be  expressed  in  generalized  coordinates  (xi,  x2,  .  .  .)  then 
r  is  a  function  of  x,  xf  .  .  .  while  R  is  a  function  of  the  co- 
ordinates and  their  first  derivatives  (x,  ±i,  x2,  .  .  .)  with 
respect  to  the  time.  Now  (R  +  r)  in  a  time  dt  follows  a  cer- 
tain path  or  sequence  of  changes  in  an  interval  of  time  dl. 
There  are  many  possible  paths  and  Hamilton's  principle  asserts 

a  path  of  "least  action"  and  is:  51    (R  —  r)dt  =  0,  where  R  —  r 

Jto 

is  the  Lagrangian  function  (L).  Consider  a  field  of  force  of 
components  FI,  Fz,  F3  due  to  a  density  distribution  of  r'0  de- 
rivable from  a  Lagrangian  function  and  K*  =  —  (v\F\  +  v^Fz  + 
v3F3)  so  that  2  (a)  vaKa  =  0. 

Instead  of  subjecting  the  system  to  the  possible  motions 
determined  by  Hamilton's  principle  they  are  subjected  to  the 
motion  defined  by  the  equation 

df(R  -  r)dt  +  J^"  K°  8x"  dt  =  °- 

ds 
Now  Einstein  shows  that  if  R  —  r  =  —  m  -j->  then  the  point 

of  mass  m  moves  as  it  would  in  a  gravitational  field.  (Einstein 
has  R  —  r  =  —  m\/^ab  gah  va  vb. 

A  large  number  of  such  material  points  free  from  each  other 
passes  into  continuously  distributed  matter  without  internal 
forces  and  the  laws  of  motion  of  such  a  system  follow  from  those 
of  a  single  point.  Let  dS  be  an  element  of  volume  in  the  exten- 
sion, then  (xi  =  dx,  Xz  =  dy,  x3  =  dz,  x±  =  dl,  K  is  the  external 
force  per  unit  volume). 


f(R  - 


K«  8x«  -    •    •  dS  =  0. 


This  would"  represent  the  general  principle  for  such  a  gravitation 
force  field. 

The  theorem  of  equipartition  of  energy  refers  to  the  distribu- 
tion of  energy  among  the  coordinates  of  a  system.  Consider  a 
system  to  be  described  by  a  large  number  n  of  coordinates  (ari, 
x2,  .  .  .  )  and  n  momenta  and  that  the  energy  is  a  homogenous 
quadratic  function  of  the  x's  and  the  momenta.  Separate  from 
the  energy  all  the  squared  terms  involving  coordinates  and 
momenta  (the  R'»),  and  take  two  sets  of  a  large  number  of  these 


ELECTROMAGNETIC  THEORY  OF  RADIATION  77 

terms  xR  and  yR,  then  the  law  of  equipartition  states  that  the 
average  of  the  xR't  is  the  same  as  the  average  of  the  yR',. 
This  law  has  been  applied  to  a  large  number  of  different  systems 
as  for  instance  the  condition  of  an  electron  atmosphere  in  a 
metal,  the  surrounding  gas  and  the  radiation  wavelengths  of 
radiation  without.  It  is  questionable  if  this  application  is 
justifiable  because  the  selection  of  the  xR'3  and  yR'a  should  not 
be  exclusive  so  that  the  xR's  are  chosen  from  among  the  electrons 
in  the  metal  and  the  yR's  from  among  the  gas  molecules. 
However  it  is  remarkable  that  the  law  does  give  us  accurate 
results  such  as  the  Rayleigh  law  for  long  wavelength  radiations. 
The  general  elementarquanta  theory  is  of  somewhat  this  type 
(Wilson).  If  Xi,  x2,  .  .  .  xj  are  the  positional  coordinates  of  a 
material  system  and  Zi,  22,  .  .  .  zj  are  the  impulse  coordinates, 
then  the  steady  periodic  motion  of  the  system  (or  of  an  ensemble 
of  elementary  systems  of  this  kind)  is  such  that  each  plane  is 
divided  into  regions  of  equal  probability,  the  mean  value  of 


which  for  any  state  of  the  system  is  -          z^dxi  =  h   (a  uni- 

versal constant).  Each  system  is  conservative  except  at  very 
short  intervals  when  it  absorbs  or  emits  energy.  During  the 
conserved  periods  the  system  follows  the  Hamiltonian  dynamics. 

During  the  critical  epochs  J  z\dx\  =  ph,  J  z2dxz  =  oh,   i  z3dx3  = 

rh,  ptff  and  r  are  positive  integers  and  the  integrations  cover 
the  Xi,  Zi,  corresponding  to  the  period  1/v,-. 

From  classic  electromagnetic  theory  Schott  and  Crehore  de- 
velop an  atom  model  consisting  of  electrons  in  a  ring  rotating 
about  the  nucleus.  The  electrons  are  then  subjected  to  radial 
and  tangential  forces.  For  two  electrons  at  the  end  of  a  diam- 

eter (2a)  the  radial  force  is  e2l  —  v  2  +  sj-jj  -\  —  °  —  '     The  ra- 

dial force  vanishes  at  01  =  2(10)-10  and  a2  =  1.8(10)~8  cms. 
All  regions  for  a  greater  than  a2  or  less  than  ai  gives  a  repul- 
sion and  between  these  values  an  attraction.  The  velocity  of 
the  electron  is  independent  of  the  value  of  a.  By  slightly 
changing  classic  theory  Crehore  derives  the  constant  of  gravi- 
tation. He  considers  the  weight  of  an  atom  to  be  proportional 
to  the  kinetic  energy  of  the  electrons  relative  to  the  nucleus. 


19.  THE  ELECTRICAL  NATURE  OF  THE  ETHER  AND  THE 
HYPOTHESIS  OF  ELECTROETHONS  AND  RADIONS 

Some  of  the  characteristics  of  the  atomic  structure  of  entity 
systems  are:  the  definite  character  of  the  atom  elements:  the 
frequent  simplicity  of  the  first  order  laws  such  as  those  of  gravita- 
tion and  of  gases:  the  universal  occurrence  of  the  finer  grained 
elements  everywhere  and  the  wealth  of  lower  ordered  structure 
and  phenomena  that  accompany  what  constitutes  the  individu- 
ality of  each  of  the  atom  elements.  One  has  only  to  view  the 
earth's  surface  and  consider  that  from  the  point  of  view  of  an 
atom  element  in  the  solar  system  the  earth  itself  consists  only 
of  a  point  possessing  a  given  mass. 

As  regards  first  order  effects  the  ether  will  be  found  no  doubt 
to  possess  a  very  simple  structure  and  the  equations  of  elec- 
tromagnetic theory  indicate  that  some  of  the  properties  of  the 
ether  are  of  the  polarization  type  so  characteristic  of  electrical 
and  magnetic  phenomena.  But  at  the  same  time  it  may  not  be 
wise  to  require  too  elementary  a  structure  to  be  the  medium  of 
all  that  complex  of  radiation  and  force  fields  that  the  ether  is 
considered  to  be. 

We  will  assume  that  the  ether  in  an  ensemble  of  electroethons 
ee,  possessing  relatively  mobile  and  immobile,  negative  and  posi- 
tive characteristics  similar  to  the  elements  of  neutral  matter, 
the  electrons  e  and  the  atomic  nuclei  h.  Energy  transfer  takes 
place  through  the  interchange  of  energy  elements  r. 

These  energy  elements  or  radions  may  be  the  mobile  electro- 
ethons or  they  may  be  independent  of  these.  We  may  picture 
them  as  constituting  a  gas  whose  particles  possess  the  light  ve- 
locity and  which  constitutes  the  only  reservoir  of  energy  at  the  ab- 
solute zero  of  thermal  temperature.  The  ether,  matter  and  elec- 
trical charge  constitute  the  vehicles  for  carrying  radions.  Either 
the  radions  or  the  electroethons  constitute  that  portion  of  the 
ether  carried  by  matter  according  to  the  experiments  of  Fizeau. 

78 


ELECTROETHONS  AND  RADIONS  79 

The  ether  will  be  viewed  as  a  porous  lattice  work  that  can  be 
defined  as  stagnant  and  when  free  of  force  fields  always  propa- 
gates radiation  with  the  velocity  c.  The  electroethons  can  be 
pictured  as  resembling  the  electron  gas  as  it  exists  in  the  lattices 
of  the  conducting  metals.  The  porosity  of  the  ether  is  such  as 
to  offer  no  friction  to  the  passage  of  matter  through  it.  It  can 
be  imagined  that  even  the  e  and  h  elements  may  be  aggregates 
or  ordered  structures  of  the  ee  elements.  The  force  fields  are 
due  to  peculiar  distributions  of  polarization  of  the  ether  lattice 
whereby  the  flow  of  the  r  elements  between  the  ee,  e  and  h  ele- 
ments is  modified.  The  tangible  model  of  the  vehicles  of  the  r 
elements  is  to  consider  the  "  interior"  of  the  ee,  e  and  h  elements 
to  contain  the  r  elements  as  a  gas. 

The  interchange  of  r  elements  among  the  masses  of  matter  is 
considered  as  a  flow  of  these  elements  between  e  and  e  elements; 
e  and  h  elements,  e  and  ee  elements  and  h  and  ee  elements.  The 
outer  "atmosphere"  of  the  neutral  atoms  being  electrons  it 
follows  that  the  surfaces  of  solids  and  liquids  consist  of  an  elec- 
tron "  film."  Ordinary  mechanics,  gas,  temperature  and  sound 
phenomena  may  represent  the  interflow  of  r  elements  between 
the  e  elements,  as  long  as  potential  energy  changes  are  not  in- 
cluded. Potential  energy  is  to  be  viewed  as  a  relation  between 
r  and  ee  elements  of  the  ether  radiations  and  force  fields.  loni- 
zation  phenomena  relate  primarily  to  the  interchange  of  r 
elements  between  the  e  and  h  elements. 


The  Great  Unknown 
->f 


1.  Life   and  Mind< ^Gateways  of  the  Senses< > Physical  World. 


Worlds/ 

Neutral  Matter  (M) 

2.  Natural     Matter*-^— >Ether  Medium,  Radi-  <--— >Electrical  World 

(E+)  92  Atomic         ation  and  Force  Fields         (E-)  Electrons  and 
Nuclei  composed        composed  of  ee  and  r        Magnetons,  e  elements, 
of  h  elements.  elements. 

"Free  Space"  (S),  with  a  c  Velocity  Characteristic 

3.  Immobile  Ether< ^Energy  Elementar-< >Mobile  Ether. 

Force    fields   due  quanta.    Radiation  ag-        ee  —  elements. 

to  a  flux  of  mobile  gregates    of    e    =    h'v 

ether   and   r  ele-  groups.     Composed  of 

ments.     ee  +  ele-  r  elements. 

ments. 


80 


FUNDAMENTAL  PHYSICS 


Potential  Energy  (P)  World 


»Ionization  Phenomena. 

Motion  of  e,  and  h,  E 
+  and  E  —  elements. 
Electrical  currents  and 
magnetism.      Interme- 
diate   velocity    world. 
Interpenetrating  e 
"film"  elements, 
lonization  World. 

<  >  Electromagnetic  Ra- 
diations in  matter  and 
in  the  ether.     Largely 
e  and  ee  motions.     Ve- 
lo  cities  approaching 
but   never    considered 
to    exceed    c.     Waves 
due   to   the  interpene- 
tration    of    e    "films." 
Radiation  World. 

4.  Mechanical  Mo-<— 

tions.  Heat  and 
sound.  Radiations 
of  M  particles. 
"Contact"  Trans- 
formations be- 
tween e  elements. 
Low  velocity 
world.  Waves  due 
to  the  contact  of 
e  "films."  World 
of  Newtonian 
Mechanics. 


Radiation  "Molecules"  by  Planck's  law  are  e  =  hv  =  jhvr 
where  v  is  the  frequency  of  the  radiation  and  j  is  an  integer. 
Experiments  remain  to  tell  whether  there  is  a  "continuous" 
series  of  these  molecules  or  a  discontinuous  series  as  is  the  case 
of  matter  molecules.  The  general  atomic  theory  would  answer 
that  the  latter  condition  holds. 

The  theory  of  radions  would  lead  to  the  result  that  at  the 
absolute  zero  of  temperature  there  is  a  condition  of  equilibrium 
of  radions  between  the  atoms  of  neutral  matter  and  the  electrons 
such  that  the  radions  in  each  molecule  and  possibly  in  each  atom 
neutralize  each  other.' 


20.  SOME  OF  THE  UNIVERSAL  CONSTANTS  OF  NATURE 

The  chapter  of  the  new  science  that  has  to  deal  with  the 
determination  of  a  more  fundamental  set  of  definitions  and  units 
has  been  greatly  advanced  by  the  discovery  of  the  method  of 
studying  atoms  of  electrical  charge  and  of  the  atoms  of  natural 
matter.  These  discoveries  permit  for  the  first  time  of  the  use 
of  individual  atoms  of  electricity  and  matter  for  the  definition 
of  the  natural  fundamental  units  of  electric  charge,  and  possibly 
of  mass. 

One  of  the  previous  methods  of  defining  units  was  that  of 
selecting  a  set  of  laws  that  appeared  to  be  of  universal  applica- 
tion, carefully  determining  the  constants  of  this  law,  and  then 
defining  the  constants  in  terms  of  units  of  the  Newtonian  system 
of  mechanics.  It  has  been  in  this  way  that  the  conceptions  of 
the  Newtonian  system  has  penetrated  into  our  whole  philosophy 
of  nature  though  we  may  make  an  effort  to  view  phenomena 
independently.  An  example  of  this  was  cited  in  the  discussion 
of  Coulomb's  law  .and  the  definition  of  the  unit  of  electric  charge 
in  the  electrostatic  system  of  units.  In  this  definition  which  is 
used  in  all  theory  the  charges  are  of  unit  magnitude  when  they 
are  equal  and  act  as  point  charges  repelling  each  other  with  a 
force  of  one  dyne  while  the  dyne  is  defined  in  the  phenomena  of 
the  acceleration  of  mass  by  Newtonian  forces.  An  electric  charge 
is  thus  defined  by  means  of  a  mass  and  in  later  experiments  when 
the  ratio  of  electric  charge  to  mass  is  found  not  to  be  constant  it  is 
assumed  that  the  electric  charge  is  constant  while  the  mass 
varies.  To  be  consistent  a  set  of  units  should  be  defined  through- 
out the  whole  range  of  conditions  for  which  it  is  to  be  employed. 
Ultimately  the  units  of  the  Newtonian  mechanics  must  be  de- 
fined for  what  we  have  designated  as  the  electrical  or  energy 
worlds. 

On  account  of  Newton's  universal  application  of  gravitation 
and  the  wonderful  success  of  the  law  in  mathematical  astronomy 
it  has  frequently  been  assumed  to  be  one  of  the  most  fundamental 
laws  of  the  universe. 

F  =  a  "-=-'• 

6  81 


82  FUNDAMENTAL  PHYSICS 

F  is  the  force  of  attraction  between  masses  m  and  mf  a  distance 
r  apart  and  G  is  a  "universal  constant."  Unfortunately  this 
law  is  not  a  convenient  one  for  laboratory  study  though  it  appears 
applicable  with  great  precision  to  coarse  grained  (astronomical) 
systems.  It  has  been  suggested  that  this  law  represents  the 
"left  over  effects"  of  the  electrical  laws  of  attraction  and  repul- 
sion. At  present  we  do  not  know  whether  the  mass  of  the  elec- 
tron is  subject  to  this  law  or  whether  the  mass  of  the  natural 
atoms  of  matter  are  of  the  gravitational  type. 

The  corresponding  inverse  square  laws  for  magnetic,  electrical 
and  gravitational  attraction  furnish  a  basis  for  the  c.g.s.  units 
and  indicate  a  marvelous  simplicity  and  a  common  origin. 
The  relation  between  the  pressure  (p)  volume  (v)  and  absolute 
temperature  (T]  of  a  gas  pv  =  RT  is  of  significance  because  of 
its  interpretation  by  the  kinetic  theory  in  terms  of  the  motions 
of  the  gas  molecules  and  the  electron  atmospheres  of  metals  in 
temperature  equilibrium  with  the  surrounding  gas  and  the  ether 
radiations  of  the  black  body  type.  T  is  a  unit  in  the  c.g.s., 
thermodynamics.  There  are  many  empirical  laws  worked  out 
under  limited  conditions  that  should  be  extended  as  widely  as 
possible.  For  instance  the  time  of  electrical  contact  of  impact- 
ing steel  spheres  in  microseconds  T  =  74.7  v^r,  where  d  is  the 

diameter  and  V  is  the  velocity  of  the  spheres  in  c.g.s.  units 
is  suggestive  of  a  large  field  of  research  work.  The  laws  of 
collision  are  very  important  as  these  give  epoch  points  of  the 
laws  of  transformation  of  the  variable  elements  of  ensembles. 
The  principle  of  least  action,  Hamilton's  principle,  certain 
hydrodynamical  differential  equations,  Maxwell's  and  the  later 
electromagnetic  equations,  the  laws  of  thermodynamics,  the 
phase  rule,  Kirchoff's  radiation  propositions,  Huyghen's  wavelet 
centers,  Poynting's  law,  Provost's  theory  of  exchanges,  the  radia- 
tion laws  of  Stefan,  Boltzmann,  Wien  and  Planck  (asVe  =  hv) 
are  a  few  of  the  laws  of  nature,  the  groundwork  of  which  has 
not  been  at  all  correlated.  The  "laboratory"  black  bodies  and 
"cavities"  for  measuring  fields  of  force  should  be  carefully 
considered  from  an  experimental  point  of  view.  The  oppor- 
tunity of  employing  a  and  j8  particles  opens  a  new  region  of 
"cavities"  for  experimental  study.  The  following  are  the 
values  of  a  few  constants,  the  invariants  of  the  transformations 
amongst  the  atomic  assemblages  of  matter  and  ether.  These 


UNIVERSAL  CONSTANTS  OF  NATURE  83 

invariants  may  be  pure  numbers,  magnitudes  with  dimensions 
and  directed  magnitudes  with  dimensions. 

Electron e  =  4.774  (10)~10 

Avagadro's  constant N  =  6.062  (10) 2 

Gas  molecules  per  cm.3  at  0°C.  and  76  cm n  =  2.705  (10)1 

Kinetic  energy  of  translation  of  a  molecule  at  0°C.  E0  =  5.621  (10)~  4 
Change  of  translational  molecular  energy  per 

1°C €  =  2.058  (10)-  • 

Mass  of  hydrogen  atom m  =  1 . 66  (10)~  4 

Planck's  element  of  action h  =  6.55  (10)~" 

Wien's  constant  of  spectral  radiation Ca  =  1 .43 

Stefan-Boltzmann  constant  of  total  radiation ...     a  =  5.72  o      (10)~12 

Grating  space  in  calcite d  =  3.030  A 

The  fundamental  units  may  be  chosen  so  that  the  gravita- 
tional constant  (G),  the  velocity  of  light  (c)  in  free  space,  the 
gas  constant  (K),  Planck's  (h)  constant,  or  the  constant  of 
electrical  (&)  and  magnetic  (/*)  attraction  shall  possess  assigned 
values.  If  G  =  c  =  R  =  h  =  l  we  have  Planck's  "absolute" 
system  of  units. 

G  =  [G]m-ll3t-* 
c  =  MB-' 
R  =  [R]mlH-*6-1 
h  =  [hlmlH-1 
K  =  [K]l-*ml*t-* 

where  e  refers  to  electric  charge  and  6  to  temperature.  All  the 
dimensional  constants  can  then  be  expressed  in  terms  of  r, 
R,  h  and  K  of  the  above  constants. 

The  laboratory  has  discovered  a  large  number  of  "effects" 
for  many  of  which  a  comprehensive  theory  has  not  been  de- 
veloped. The  more  complicated  types  of  the  Zeeman  effect 
belong  to  this  class  while  the  electrostatic  Stark  effect  on  sec- 
trum  lines  is  barely  touched  by  theory,  so  complex  are  the  com- 
ponents of  effected  lines.  Indeed  the  whole  subject  of  line  and 
band  spectra  furnishes  many  worlds  for  many  Alexanders  to 
conquer,  much  more  worthy  and  requiring  higher  talent  than 
disorganized  Persias.  The  conditions  in  spectroscopy  are 
indicated  because  every  physicist  has  the  instinctive  feeling  that 
here  lies  the  answer  to  the  questions  involving  the  structure  of 
the  atoms.  All  provinces  of  scien'ce  contain  undeveloped  fields 
and  one  of  the  pressing  problems  of  the  laboratory  is  that  of  the 
development  of  apparatus  and  methods  of  attack  that  will 
permit  of  quicker  and  more  effective  offensive  movements  into 
the  regions  that  are  unexplained  and  unexplored.  - 


21.  FUNDAMENTAL  DEFINITIONS  AND  UNITS  AND  THE 
CEER  THEORY 

The  treatment  of  natural  quantities  is  made  possible  by  means 
of  assigning  certain  magnitudes  and  in  some  instances  a  sense  or 
direction  property.  The  atomic  elements  are  the  magnitudes 
that  are  smallest.  We  have  seen  that  throughout  nature  entity 
magnitudes  are  composed  of  practically  identical  elements. 
The  aim  of  the  laboratory  is  to  obtain  the  smallest  number  of 
elements  for  the  description  of  phenomena  and  to  select  these 
elements  so  that  they  can  be  the  most  universally  and  con- 
veniently used. 

In  the  past,  definitions  and  units  of  a  local  character  have 
usually  been  selected  for  given  natural  systems.  The  foot 
length  is  convenient  in  the  making  of  shoes.  The  meter  is 
adapted  to  geodetic  work.  The  definition  of  unit  density  in 
terms  of  water  or  the  unit  electric  charge  in  terms  of  the  repul- 
sion of  spheres  are  all  examples  of  convenient  local  units.  The 
great  disadvantage  of  these  local  units  is  that  they  have  been 
defined  for  different  local  systems  and  none  of  them  have  been 
based  upon  the  natural  atomic  elements.  Units  defined  in 
terms  of  the  natural  elements  would  have  their  magnitudes  and 
perhaps  their  sense  qualities  frequently  expressed  in  a  one  to 
one  correspondence  to  the  elements  themselves.  Suppose  that 
the  unit  of  electric  charge  is  defined  in  terms  of  the  charge  of 
the  electron.  Every  number  representing  an  electric  charge 
would  then  be  a  positive  or  negative  integer. 

A  natural  system  of  units  would  then  always  employ  integers 
in  the  expression  of  the  elements  used  for  the  definitions.  If 
the  finest  grained  elements  are  employed  in  the  determination 
of  the  units  then  all  magnitudes  and  senses  or  directions  would 
be  expressed  in  terms  of  integers.  This  is  the  general  atomic 
theory  of  natural  philosophy  and  this  philosophy  is  being 
continually  supported  by  experiment.  In  so  far  as  it  is  sup- 
ported by  experiment  it  is  a  part  of  the  new  science. 

The  smallest  number  of  natural  elements  required  to  explain 
phenomena  constitute  the  ensemble  of  defining  elements. 

84 


FUNDAMENTAL  DEFINITIONS  85 

Whether  there  is  a  unique  ensemble  of  this  kind  or  whether  a 
number  of  equally  simple  ensembles  will  be  available  remains 
for  experiment  to  determine.  At  any  rate  we  may  aim  to  select 
our  laboratory  definitions  and  units  from  the  most  universally 
distributed  and  fine  grained  of  the  entity  elements. 

The  transformations  between  the  entity  systems  have  been 
found  to  be  of  two  types,  contact  transformations  taking  place 
during  the  collisions  of  matter  (apparently  described  by  the 
Newtonian  mechanics  when  the  velocities  concerned  are  com- 
paratively small  and  new  electromagnetic  laws  when  the 
velocities  are  high)  and  the  ether  transformations  which  take 
place  between  portions  of  matter  that  may  be  at  great  distances 
from  each  other.  If  we  are  to  view  the  outer  parts  of  atoms  as 
being  constituted  of  rotating  electrons  and  an  ether  more 
or  less  modified  by  the  presence  of  the  atom  (and  this  condition 
is  supported  by  experiments  as  far  as  they  go),  then  contact 
transformations  possess  an  electrical  and  ether  quality.  Then 
if  experiments  indicate  that  the  ether  is  electrical  in  character 
it  may  follow  that  all  natural  transformations  possess  an  elec- 
trical quality.  Assuming  that  both  contact  and  ether  trans- 
formations are  electrical  and  that  these  transformations  are 
universal  for  all  the  entity  systems  of  the  universe  it  follows 
that  our  definitions  and  units  should  be  selected  to  make  our 
scientific  laws  simulate  these  contact  and  ether  transformations 
as  closely  as  possible. 

The  conditions  of  energy  interchange  also  suggests  that  if 
possible  our  definitions  and  units  should  describe  these  inter- 
changes as  simply  as  possible. 

The  elements  appearing  in  all  natural  changes  then  appear 
to  be  the  vehicles  of  electrons  and  the  atoms  of  natural  matter, 
the  carrier  or  the  ether  and  the  elements  that  appear  and 
disappear  among  the  ensemble  of  ether,  electrons  and  the 
natural  atoms.  Whether  any  of  these  elements  are  absolutely 
conserved  will  remain  for  experience  to  decide.  Our  present 
theories  usually  accept  the  view  that  the  electron  as  regards  its 
electrical  charge,  the  natural  atoms  as  regards  their  simple 
elements  such  as  possibly  the  hydrogen  and  helium  nuclei  and 
the  ether  of  free  space  are  absolutely  conserved,  the  unchanging 
elements  of  an  eternal  universe. 

The  elements  that  are  variable  and  that  appear  and  disappear 
such  as  kinetic  energy,  potential  energy  and  the  radiation  quanta 


86 


FUNDAMENTAL  PHYSICS 


are  certain  changes  among  the  absolutely  conserved  elements 
that  are  to  be  measured  by  magnitudes  such  as  mass,  time, 
velocity,  acceleration  and  temperature. 

The  following  table  defines  certain  physical  magnitudes  in 
terms  of  certain  elementary  units,  e,  the  electrical  charge  of  the 
electron  (or  perhaps  eventually  ee  of  the  ether);  c,  the  velocity 
of  light  and  r  the  element  of  energy,  e  possesses  a  +  and  — 
sense  while  c  and  r  are  directed  elements  and  may  be  employed 
to  define  the  three  elements  of  extension. 


DIMENSIONS  OP  LABORATORY  UNITS 


Laboratory  assumed  to  be  at  rest 


(Laboratory  with  velocity  /3 


C  ff  8  k 

. 

CKse 
c.g.s.e. 

.e.r. 

' 

ransverse 

ongi  u  ina 

Geometrical: 
Length  
Area  

I 
J" 

I 

I* 

d 

d* 

eV-i 
eV-2 

62r-l 

e<r-J 

z<vr^=z 

b 

Volume  
Kinematical: 
Time 

I* 
t 

l> 
t 

d' 
c'M 

eer-4 

c-le2,.-l 

e»r-« 
eV-i 

(tf  —  tt) 

\/l    02  =  ( 

Velocity  
Acceleration  .  .  . 
Mechanical: 
Mass  

Momentum.  .  .  . 
Force 

ft-» 
U-i 

m 

mU~l 
mlt~* 

«-i 

ft-* 

TO 
TO«-» 

ndr* 

c 
c*d-i 

c-»d->e» 

c-id-'ez 
d-W 

c 

&e-iT 

c-V 

c~lr 
e~V2 

I 

e-*r 

r 

r 
e~Vl 

m<  = 
Vl-^2m 

w/d-Wi 

Energy  
Pressure  
Electrical: 
Charge  
Potential  
Capacity  

mlH-* 
ml-H-* 

tliimlr» 
t-Wmiri 

kl 
k 

min-* 

ml-H-* 

e 
J'mr*e-» 
en-*m-H* 
en-'m'H1 

d-"e' 
d-««z 

e 
d-'e 
d 

r 

e-tft 

e 
e~'r 
eV"1 

r 
e-«r« 

e 
e-ir 
e*r-' 

Current  
Resistance  
Electric  field... 
Magnetic  field.. 
Magnetic  pole.  . 
Permeability  .  . 

k\tim\t-* 
k-U 

*-lHmlr> 

t'rimir* 

k-\ttm\ 
I 

ell-* 
e-*lmt-i 
6-imZT* 
eJ-U-i 
e-'2*mri 
e-»/m 

cd-^e 
c'1 
d~*e 
d-*e 
e 

ce~lr 
c'1 
e-*r* 
e~*r* 
e 

e->r 

z 

e-«r« 

e-»r2 
«• 

The  first  column  of  dimensions  gives  the  values  as  obtained  in 
the  electrostatic  system  by  using  Coulomb's  law  and  the  funda- 
mental units  are  taken  as  inductivity,  length,  mass  and  time.  In 
the  second  column  the  fundamental  units  are  electric  charge, 
length,  mass  and  time.  For  the  medium  where  the  inductivity 
remains  constant  this  quantity  can  be  omitted  from  considera- 
tion as  is  done  in  the  last  five  columns. 


FUNDAMENTAL  DEFINITIONS  87 

There  is  in  common  use  two  systems  of  units,  the  electrostatic 
and  the  electromagnetic  according  as  the  inductivity  or  the  per- 
meability are  used  as  dimensions.  If  m,  I  and  t  are  given  integral 
exponents  then  the  inductivity  appears  as  an  elasticity  and  the 
permeability  as  a  density  or  vice  versa.  There  is  no  alternative. 
Corresponding  to  this  condition  is  that  relating  to  the  directions 
of  the  ether  vibrations  and  the  problem  as  to  whether  electrical 
energy  is  potential  and  the  magnetic  energy  kinetic  or  vice  versa, 
using  the  vibrations  of  a  mechanical  system  as  the  pendulum  as 
an  analogue.  Either  the  electric  or  the  magnetic  fields  can  be 
represented  by  a  mechanical  analogue  but  the  relations  of  the  two 
fields  cannot  be  so  represented. 

In  the  third  column  the  fundamental  units  c,  the  velocity  of 
light  in  free  space,  rf,  the  diameter  of  the  electron  and,  e,  the  charge 
of  the  electron  are  considered  as  the  natural  units.  In  the 
fourth  column  the  fundamental  units  are  taken  as  c,  e  and  r  the 
energy  of  the  radion.  lie  is  ever  found  to  be  a  multiple  of  a  unit 
such  as  ee  then  ee  would  become  the  natural  unit  of  charge.  This 
system  will  be  called  the  absolute  system  of  natural  units  because 
it  lays  at  the  bottom  of  our  laboratory  experience  that  these 
natural  elements  are  absolutely  conserved  and  are  constituted  of 
identical  atoms. 

The  laws  upon  which  the  above  system  of  units  are  based  are 
the  laws  of  our  own  laboratories  which  we  consider  invariably  at 
rest  when  making  experiments.  Our  mechanics  indicate  that 
motion  is  relative  and  that  by  mechanical  means  we  cannot  ob- 
serve the  velocity  of  any  laboratory  by  experiments  made  in 
that  laboratory.  Electrical  experiments  indicate  that  the 
assumption  that  electrical  charge  remains  constant  gives  a  con- 
sistent explanation  of  phenomena  and  if  there  is  discovered  an 
element  of  mass  that  is  found  to  be  conserved  then  that  element 
can  be  employed  as  an  absolute  unit.  Experiments  also  indicate 
that  we  cannot  measure  the  motion  of  our  system  by  measuring 
the  velocity  of  light  in  different  directions. 

When  we  consider  that  the  kinetic  energy  of  a  system  is  meas- 
ured in  terms  of  we2  and  that  the  value  of  this  energy  is  relative 
to  the  way  the  velocity  of  a  system  is  measured  it  follows  at  once 
that  I,  m  and  t  must  necessarily  be  relative  to  each  other  and  the 
velocity  given  to  the  laboratory  if  our  assumed  laws  of  r  and  c  are 
to  hold.  A  relative  theory  based  on  these  conditions  will  be 
outlined  shortly. 


88  FUNDAMENTAL  PHYSICS 

The  application  of  such  a  relative  theory  for  electromagnetic 
theory  is  complicated  by  our  not  knowing  the  dimensions  of  the 
permeability  and  the  inductivity  hence  the  relative  theory  as 
applying  to  the  electrostatic  system  is  developed. 

An  interesting  application  to  ancient  cosmosgony  may  be 
noticed  to  relate  to  the  definition  of  time  in  the  cer  units,  there 
being  the  beginning  of  time  when  it  was  said,  "Let  there  be  light." 

Consider  two  laboratories  LI  and  L2  moving  with  a  relative 
velocity  of  v  cm.  per  sec.  or  with  /3  units  velocity  according  to  the 
r  dimensions  in  terms  of  c  =  1,  the  observing  angels  A\  and  A2 
in  LI  and  L2,  respectively,  considering  themselves  to  be  at  rest. 
The  relative  velocity  /3  must  indicate  that  if  this  velocity  is 
apportioned  to  the  two  laboratories,  the  laboratories  must  move 
along  parallel  paths  (parallel  paths  being  defined  as  the  paths  of 
two  light  beams  from  two  stars  whose  distance  from  the  labora- 
tory telescope  is  too  great  to  be  measured  by  any  means  such  as 
the  parallex  method  and  the  stars  are  so  close  together  that  they 
can  just  be  resolved.  This  may  be  taken  as  a  definition  of  parallel 
lines).  Only  when  three  or  more  laboratories  are  concerned  does 
relative  motion  other  than  along  two  parallel  lines  require  to  be 
considered.  The  relative  method  could  then  define  the  units  of 
one  laboratory  as  being  absolute. 

The  parallel  paths  of  Li  and  L2  define  a  direction  and  mechanics 
such  that  A  i  and  A2  agree  in  their  measurement  of  the  distance 
between  these  lines. 

Let  Ai  and  Az  define  a  unit  of  time  as  the  time  required  to 
traverse  a  distance  equal  to  the  diameter  of  an  electron  d. 


Li 


A  i  assumes  he  is  at  rest  and  that  the  light  track  is  di  perpendicular 
to  the  direction  of  their  relative  motion.  A  2  considers  his  light 
track  d2,  AI  considers  however  that  while  the  light  traversed  d? 
the  laboratory  moved  to  b  where  bd  represents  the  velocity  of  the 

laboratory.     The  unit  of  his  own  time  A  i  considers  to  be  -^  =  t\. 
A  2  "considers"  his  unit  to  be  —  =  t2  because  he  thinks  he  is  at 


FUNDAMENTAL  DEFINITIONS  89 

rest  but  A  i  says  that  his  unit  is  really  —  =  1 2  and  is  therefore  too 

c 

large,  di  =  d2. 

Hence  (1)         tz  Vl  -  /32  =  ti         (to  terms  in  /34) 

In  any  laboratory  it  is  assumed  that  the  time  intervals  are 
independent  of  the  "direction"  in  which  they  are  measured  so 
that  relation  (1)  can  be  applied  to  "  longitudinal"  time  if  we  wish 
to  think  of  such  a  unit. 

As  j  =  ci  and  j  =  c2,  from  (1)  if  Ci  =  c2  we  have  12  \/l  —  ft* 
=  h  (2). 
Let  A  i  send  a  radion  of  momentum  MIC  to  A2  who  determines 

its  momentum  in  his  laboratory  to  be  M 2c,  MI  ^  =  M2  T  whence 

t\  it 

MI  =  M2\/l  —  /32  (transverse  masses)  (3) 

Consider  A\  and  A 2  each  having  a  radion  with  the  velocity 
of  c2  in  the  same  direction  as  ft.  A\  considers  the  energy  of 
his  to  be  Afi(c2  =  1)  and  A2  his  to  be  M2(c2  =  1).  But  AI 
claims  that  A2's  radion  must  have  M$z  more  energy  than  what 
his  radion  possesses  and  hence  is  too  large.  So  M\  varies  as 
(1  —  (32)M2  where  the  values  of  M\  and  M2  are  to  be  viewed  as 
in  (3),  'A  i  not  only  considering  that  Az  has  not  correctly  indicated 
the  energy  of  his  system  but  that  his  masses  are  to  be  considered 
by  (3)  so  that  MI  =  (1  -  p*)y*Mz  (longitudinal  mass)  (4) 

The  definition  of  time  by  means  of  the  velocity  of  a  light 
wav~e  immediately  indicates  the  difficulty  of  defining  the  simul- 
taneity of  events  that  occur  in  two  different  systems.  Consider 

/                  C  ^\ 

that   (A. — •  B  — > )  A  2  arranges  in  his  laboratory 

vibrating  atoms  or  other  suitable  time  measuring  apparatus.  He 
regulates  these  from  C  where  AC  =  CB  =  d.  A2  defines  the 
"atoms"  at  A  and  B  as  vibrating  synchronously.  A-i  considers 
AC  =  CB  =  d\/l  —  |82.  A  i  also  considers  that  in  "setting" 
the  atoms  the  velocity  of  the  signal  in  going  from  C  to  A  was 
1  —  /3  and  from  C  to  B,  1  +  0.  AI  considers  that  the  clock 
(or  atom)  at  B  is  too  slow  and  A  is  too  fast,  the  difference  in 

time  being  d  V^f?  (^  -  j™)  =  ^=  (5) 

Let  AI  establish  coordinates  on  his  system  of  x\,  y\,  Zi,  t\ 
and  Az,  £2,  2/2,  22,  £2  where  x  is  in  the  direction  of  ft.  As  it  has 


90  FUNDAMENTAL  PHYSICS 

been  assumed  that  the  distance  between  the  laboratories  is 
found  to  be  the  same  by  A\  and  Az,  y^  =  y\  and  22  =  z\>  A.\ 
considers  a  point  appearing  to  be  at  x\  from  the  yzz2  plane 
at  time  ti  =  0.  When  t  =  ti  the  point  will  appear  to  be  at 
x\  —  pti  from  the  y2z2  plane.  A2  considers  this  distance  to 
be  x-t  because  he  considers  himself  to  be  at  rest  and  from  (2) 
£2\/l  —  /32  =  Xi  —  /3<i.  To  AI  considering  the  point  x\  from 
the  ytfi  plane  at  t  =  t\  the  clock  on  L2  at  the  same  distance  Xi 

from  y\z\  appears  by  (5)  to  be  slow  by  the  amount  —  -  and  in 
the  units  of  L\  this  clock  would  register  \i\  --  -  j  time.  From 

(1)  tz  \/l  —  ft*  =  t\  --  -•     From  these  relations  are  obtained 

the  equations  of  transformation  of  coordinates  of  two  systems 
in  relative  motion. 


, 

" 


These  are  sometimes  written  in  the  form  where  a  =  - 


,  .-02 
tz  =  <*(*!-  ^)       x,  =  aCsi-jS*!)     2/2  =  yi   and  z2  =  z, 

In  electrodynamics  the  fundamental  laws  are  left  unaltered 
When  the  coordinates  of  AI  are  changed  to  those  of  A2  and  vice 
versa.  For  dynamical  phenomena  the  equations  are  x2  =  Xi 
—  utij  2/2  =  2/1  —  vh>  z2  =  z\  —  ut\  and  t%  =  ti  (where  u,  v, 
u  are  the  components  of  the  relative  velocity)  and  transforma- 
tions of  these  coordinates  leave  the  equations  defining  the  units 
unaltered. 

It  has  been  suggested  that  the  fundamental  units  might  be 
such  that  a  miniature  reality  could  be  constructed  that  would 
faithfully  simulate  what  we  consider  such  to  be.  But  this  view 
is  dispelled  immediately  when  we  select  a  natural  set  of  units  such 
as  e,  c  and  r.  The  ultimate  e  entity  is  so  gross  that  individuals  of 
them  can  be  studied  for  minutes  at  a  time.  Any  hypothetical 
reality  in  miniature  must  therefore  be  constructed  above  the 
threshold  of  'appearance  of  the  natural  units  and  this  is  of 


FUNDAMENTAL  DEFINITIONS  91 

course  only  possible  for  very  small  sections  of  reality  such  for 
instance  as  the  picturing  of  the  atom  as  a  miniature  solar  system. 
Transformations  of  this  kind  are  most  successful  when  comparing 
very  gross  with  fine  grained  entities. 

The  definitions  and  units  of  science  can  be  selected  in  a  number 
of  ways  and  until  the  experimental  fields  have  been  carried  into 
the  finest  grained  structures  the  framework  of  science  cannot  be 
said  to  be  complete.  The  following  treatment  is  to  be  considered 
as  suggestive  of  the  way  the  axioms  of  science  will  be  laid  when 
we  know  the  structure  of  the  ether  and  of  radiation. 

The  smallest  known  element  in  the  laboratory  is  the  electron, 
e.  Evidence  is  accumulating  that  the  atomic  nuclei  may  be  com- 
posed of  hydrogen  and  helium.  For  simplicity  consider  the 
atoms  to  consist  of  elements,  h,  and  to  be  endowed  with  the 
properties  that  we  ascribe  to  positive  electricity.  The  h  element 
is  much  less  mobile  than  the  e  element.  Experiments  indicate 
that  ordinary  matter  atoms,  M,  possess  the  structure  M  =  xe- 
+  [yh  +  e  (x  —  y}],  the  part  within  the  nucleus  being  represented 
by  the  term  in  the  brackets.  This  equation  will  be  called  con- 
dition or  law  II. 

Law  1.  M  =  x(e-}  +  [y(e  +)  +  (x  -  y)  (e-)} 

The  ether  (S)  will  be  considered  as  analogous  and  a  more  fine 
grained  structure  than  neutral  matter  and  its  elements  will  be  the 
electroethons,  ee  +  and  ee  —  similar  to  e  and  h. 

Law  2.  S  =  2x    (ee  +)  -f  2x    (ee  -) 

The  radiation  or  energy  elements  (r)  will  be  considered  as  the 
finest  grained  of  all  the  structures  and  they  are  assumed  to  pos- 
sess conserved  extension  properties  and  will  be  denoted  by 
eee  +  x,  eee  +  y,  eee  +  z,  eee  —  x,  eee  —  y,  and  eee  —  z  as 
previously  described. 

Law  3.  r  =  S  eee's 

For  the  ether  we  have  the  condition  law  of  the  neutralization 
of  ee  +  and  ee  — .  For  radiation  the  law  3  of  the  neutralization 
of  elements. 

A  point  is  defined  as  the  "  location  "  of  an  r  element  in  the  ether 
lattice  framework  or  in  space,  A  point  at  rest  in  the  location  of  a 
neutralized  set  of  r  elements  preferably  as  simple  as  possible. 
The  points  are  to  be  considered  as  without  size  or  shape  or  struc- 


92  FUNDAMENTAL  PHYSICS 

ture  because  there  is  no  means  for  indicating  such  qualities  as 
the  points  are  not  the  source  or  sink  of  any  radiation. 

The  function  of  the  ee  ensemble  is  that  of  the  electromagnetic 
medium,  it  being  here  assumed  that  phenomena  such  as  gravita- 
tion are  of  this  type.  These  phenomena  are  considered  as  due  to 
electroethon  collisions  and  that  the  history  of  these  collisions  is 
given  by  the  interchanges  of  the  r  contents  of  the  electroethons 
during  collision. 

The  path  of  any  moving  point  of  an  r  carrier  that  does  not  re- 
ceive or  lose  any  r  elements  is  defined  as  a  straight  line.  Pos- 
sibly the  lattice  structure  of  the  ee  ensemble  could  also  serve  to 
define  straight  lines  and  directions.  These  properties  have 
however  been  assigned  to  the  r  elements.  The  path  of  a  light 
ray  in  the  ee  ensemble  could  be  used  to  define  a  straight  line  and 
this  is  constantly  done  in  surveying.  A  line  of  force  in  the 
ether  field  such  as  the  plumb  line  is  adapted  for  this  service.  The 
opportunity  of  using  different  methods  makes  it  possible  to  check 
the  definitions  whenever  the  laboratory  facilities  are  developed 
sufficiently. 

Rotations  require  the  flow  of  radions  due  to  their  varying  den- 
sity in  the  force  fields.  Thus  the  radion  maintains  its  own  energy 
as  regards  direction  and  magnitude  unchanged.  The  magnitude 
of  its  energy  is  assumed  to  be  ic2  and  its  direction  is  employed 
to  define  the  extension  directions,  these  directions  to  harmonize 
with  directions  as  given  by  the  ether  lattice. 


22.  THE  THEORY  OF  ELEMENT ARQUANT A 

In  the  time  of  Newton,  one  of  the  most  serious  objections 
offered  to  the  wave  theory  of  light  was  its  apparent  failure  to 
explain  the  formation  of  shadows.  Sound  and  water  waves  were 
known  to  show  diffraction,  whereas  at  that  time  all  evidence 
favored  the  view  that  the  propagation  of  light  was  rectilinear. 
This  objection  was  removed  by  Huyghens  and  Fresnel. 

Huyghens  regarded  every  vibrating  point  on  the  wave  front 
as  the  center  of  a  new  disturbance.  These  secondary  disturb- 
ances travel  with  the  same  velocity  and  are  enveloped  by  a  sur- 
face which  is  identical  with  the  surface  from  which  the  secondary 
disturbances  started.  The  enveloping  surface  forms  the  new 
wave  front.  This  view  of  wave  propagation  is  Huyghen's  prin- 
ciple. Using  the  principle  of  interference  discovered  by  Young, 
by  which  is  meant  the  fact  that  two  luminous  vibrations  may 
destroy  each  other,  Fresnel  explained  the  phenomena  of  shadows 
on  the  theory  that  there  was  destructive  interference  between 
the  secondary  wavelets  in  the  region  of  the  shadow. 

The  secondary  wave  apparently  lies  wholly  in  front'of  the  plane 
tangent  to  the  wave  front  at  the  center  of  the  wavelet  and  the 
effect  is  supposed  to  be  greatest  on  the  normal  to  the  wave  surface 
drawn  to  the  center  of  the  wavelet.  This  applies  to  a  medium 
that  is  transparent. 

The  presence  of  charges  in  a  medium  either  as  ions  or  electrons, 
that  can  be  set  into  vibration  by  the  light  wave,  results  in  ab- 
sorption. This  absorption  may  be  considered  as  the  frittering 
away  of  the  light  energy  which  is  necessary  to  overcome  the 
friction  that  accompanies  the  motion  of  the  ions.  In  the  equa- 
tions from  which  the  dispersion  formulae  are  derived,  all  that  is 
necessary  to  assume  is  that  the  motion  of  the  ions  is  accompanied 
by  damping.  As  to  the  nature  of  this  transformation  of  energy 
nothing  is  assumed,  although  it  can  be  shown  that  the  vibrations 
of  electrons  may  be  damped  during  molecular  impacts. 

The  radiation  from  the  ions  set  into  vibration  by  the  light 
wave  is  emitted  in  all  direction,  and  thus  differs  essentially  from 
the  secondary  waves  of  Huyghens.  Planck  has  treated  this 


94  FUNDAMENTAL  PHYSICS 

subject  and  shows  how  the  energy  of  the  advancing  wave  is 
reduced  by  the  back  radiation  of  the  electrons.  This  absorption 
would  not  be  a  transformation  of  the  energy  into  kinetic  energy 
of  molecular  motion.  In  the  treatment  of  Planck  the  phase  of 
the  vibrating  ion  is  considered  as  lagging  a  quarter  of  a  period 
behind  that  of  the  exciting  waves  besides  the  lagging  of  the 
radiation  of  the  electron  itself  by  a  quarter  of  a  period  behind  its 
own  vibration.  Planck  applies  his  theory  in  general  to  resona- 
tors, so  that  we  may  use  the  term  resonator  in  place  of  that  of 
the  electron  or  ion.  The  wave  emitted  by  a  system  of  resonators 
will  thus  be  a  half  wavelength  behind  that  of  the  exciting  waves, 
and  will  be  in  a  condition  to  produce  interference.  Planck's 
treatment  differs  from  that  of  Drude  in  that  the  damping  is 
referred  to  radiation  entirely. 

Since  the  work  of  Huyghens,  the  wave  theory  of  light,  based  on 
an  elastic  or  electromagnetic  ether,  has  been  found  to  be  in  such 
good  accord  with  experiment  that  the  old  emission  theory  of 
Newton  was  abandoned.  The  work  of  Maxwell  and  Hertz  has 
given  the  wave  theory  an  electromagnetic  interpretation.  The 
theory  as  thus  modified  explains  reflection,  refraction,  inter- 
ference, polarization,  etc.  The  theory  has  recently  been  modified 
again  by  the  addition  of  the  relativity  hypothesis  in  order  to 
explain  aberration,  the  experiments  of  Airy,  Fizeau,  and  Michel- 
son  and  Morley.  This  hypothesis  states  that  the  equations 
representing  the  laws  of  nature  remain  the  same,  whether  the 
system  of  coordinates  remains  at  rest  or  in  motion.  These  theo- 
ries view  electromagnetic  radiation  as  continuous. 

On  the  other  hand,  there  are  reasons  for  assuming  the  radiation 
of  energy  .to  be  in  elements  of  an  electromagnetic  nature  some- 
what resembling  material  particles.  Planck  assumes  that  a 
radiating  body  contains  a  large  number  of  resonators  and  that 
these  may  lose  or  gain  energy  in  finite  amounts,  the  portions  of 
energy  e  depending  on  the  frequency  of  the  resonators  v  and  a 
universal  constant  h, 

e  =  hv. 

The  ionization  produced  by  z-rays  and  ultraviolet  light 
would  be  expected  to  be  distributed  uniformly  over  the  wave 
surface,  all  the  atoms  exposed  to  the  radiation  suffering  the  same 
change.  As  this  is  not  the  case  it  has  been  suggested  by  Thom- 
son and  others,  that  the  energy  is  not  uniformly  distributed  on 
the  wave  front  but  that  it  is  concentrated  into  various  points 


THE  THEORY  OF  ELEMENTARQUANTA  95 

on  the  wave  surface.  This  kind  of  distribution  of  energy  in  the 
wave  front  would  result  in  the  same  effect  as  would  be  expected 
from  the  hypothesis  that  energy  is  radiated  in  finite  magnitudes. 
One  of  the  difficulties  confronting  the  theory  of  finite  elements 
of  energy  is  its  apparent  irreconcilability  with  the  Maxwellian 
equations  of  electrodynamics.  In  the  earlier  forms  of  the  theory 
of  elementarquanta  the  emission  of  the  elements  of  energy  is 
assumed  to  be  excited  by  the  continuous  absorption  of  energy 
from  the  incident  radiation  upon  one  of  the  assumed  oscillators. 
Planck  has  also  assumed  that  absorption  and  emission  are  en- 
tirely independent.  Emission  is  assumed  to  take  place  sponta- 
neously in  amounts  e  —  hv.  The  calculus  of  probabilities  can 
then  be  applied  and  the  probability  of  the  emission  of  an  element 
e  by  an  oscillator  of  frequency  v  in  a  time  dt  (which  is  small  com- 
pared with  the  interval  between  two  successive  emissions),  is 
yndt,  rj  being  a  constant  of  the  oscillator  and  n  the  number  (a 
positive  integer)  of  elements  of  energy  originally  contained  in  the 
oscillator.  If  u  is  the  vibrational  energy  of  the  oscillator,  n  will  be 

such  that  (  --  n\  is  a  positive  real  proper  fraction. 

The  energy  absorbed  in  a  time  dt  cannot  be  equated  to  the 
energy  emitted  in  the  same  time  if  the  former  varies  continuously 
and  the  latter  by  increments.  Let  <p  be  the  entropy  of  the  oscil- 
lator, and  w  the  probability  of  the  oscillator  having  an  amount  of 
energy  u,  then  <p  =  k  log  w  where  k  =  1346(10)~16  erg/degree. 
The  new  hypothesis  gives  the  mean  value  of  u,.  u,  at  the  absolute 
temperature  T  as  being 

hv 

hv  em  +  1 


This  value  of  u,  differs  from  that  of  the  old  theory  by  the 

hv 
appearance  of  the  additive  constant  -^' 

The  theory  involves  the  emission  of  energy  in  quanta  in  case 
of  electronic  motions  as  well  as  radiation  and  the  apparently 
constant  energy  of  the  a  and  0  particles  confirm  this  hypothesis. 

The  problem  of  the  equipartition  of  energy  between  the  vari- 
ous degrees  of  freedom  is  one  that  remains  unsolved.  One  way 
of  avoiding  the  problem  is  to  consider  that  the  degrees  of  free- 
dom that  are  connected  with  radiational  phenomena  are  in- 


96  FUNDAMENTAL  PHYSICS 

operative  under  ordinary  thermal  conditions.  The  "steady" 
supply  of  energy  of  one  form  and  the  steady  loss  in  another  form 
under  experimental  conditions  is  given  by  Planck's  law  for  the 
distribution  of  energy  among  the  various  wavelengths  of  radia- 
tion. Planck  attributes  the  failure  in  the  application  of  the  law 
of  equipartition  to  the  nature  of  energy  itself,  some  degrees  of 
freedom  absorbing  no  units  of  energy  and  other  freedoms  ab- 
sorbing an  unequal  number  of  units  in  some  cases.  Planck's 
theory  leads  to  the  law  for  the  distribution  of  energy  among  the 
various  wavelengths  in  black  body  radiation.  It  may  also 
mean  that  molecular  and  atomic  motions  must  be  discontinuous. 

Planck's  theory  represents  the  radiation  coming  from  a  solid 
as  due  to  a  very  great  number  of  Hertzian  resonators.  Each 
resonator  has  its  own  characteristic  period,  and  emits  a  rigor- 
ously monochromatic  radiation.  In  consequence  of  the  changes 
of  energy  between  the  resonators,  there  is  established  a  parti- 
tion of  energy  following  a  certain  law,  and  there  also  results  a 
certain  distribution  of  radiant  energy  throughout  the  spectrum, 
although  the  resonators  neither  absorb  nor  emit  any  radiation 
except  that  which  is  characteristic  to  them.  The  exchange  of 
energy  takes  place  by  the  Doppler  principle,  either  the  resonators 
being  in  motion,  or  the  radiation  is  reflected,  refracted,  diffracted 
or  diffused  by  bodies  in  motion;  and  by  mechanical  phenomena 
such  as  collisions.  It  is  not  supposed  that  the  resonators  have 
any  direct  influence  on  each  other,  but  that  the  exchanges  of 
.energy  will  be  made  through  the  interaction  of  matter. 

The  relation  between  the  radiation  formulae  of  Wien  and  Ray- 
leigh  were  indicated  by  Planck  who  imagines  an  enclosure  filled 
with  black  body  radiation  and  bounded  by  perfectly  reflecting 
walls.  Within  the  enclosure  the  linear  electromagnetic  oscillators 
of  frequency  v  are  in  equilibrium  with  the  black  body  radiations. 
The  energy  of  any  radiator  Ev  and  the  energy  per  unit  of  volume 
ev  of  radiation  of  frequency  v  is 


Now  assume  that  Ev  is  composed  of  an  integral  number  of  elemen- 
tary units  of  energy  c.  From  a  consideration  of  the  number  of 
oscillators  and  the  number  of  elementary  units  of  energy  it  fol- 
lows that  the  value  of  the  entropy  of  the  system  is: 


THE  THEORY  OF  ELEMENTARQUANTA  97 

From  the  second  law  of  thermodynamics  as  applied  by  Wien 


Hence  it  follows  that  the  elementary  unit  of  energy  is  propor- 
tional to  the  natural  frequency  of  the  oscillator,  e  =  hv,  h  being 
a  universal  constant. 

Planck  then  derives  his  formula, 


For  small  values  of  X  this  becomes  Wien's  equation 


fj      TTTFl 

and  for  large  values  of  XT7  Rayleigh's  equation,  Ex  =  —^  —  . 

From  the  theory  a  correct  energy  distribution  curve  is  obtained 
and  the  value  of  the  unit  charge  of  electricity  can  be  calculated 
from  the  radiation  constants. 

The  theory  of  elementarquanta  haw  been  developed  as  essen- 
tially related  to  the  problems  of  radiation  and  the  picture  of  the 
resonators  has  not  been  correlated  with  the  nature  of  the  atom 
structures  as  we  know  them.  The  theory  is  susceptible  to  a  much 
wider  interpretation  than  that  of  explaining  the  variation  of 
radiation  with  temperature. 

Assume  that  the  atomic  structure  of  energy  is  ultimately 
kinetic,  conserved  and  constituted  of  directed  radions.  Then 
Planck's  e's  are  the  "molecules"  of  energy  and  the  law  is  e  = 
hv  =  nr  where  n  is  a  positive  integer.  Then  the  partition  of 
energy  would  take  place  only  during  the  collisions  of  portions  of 
matter  either  in  the  neutral  or  electrical  states  or  in  the  so-called 
unstable  or  radiating  states  of  matter  due  to  collisions  or  to  ether 
transmission.  Assuming  electroethons  we  can  make  partition  of 
radions  a  collision  phenomena.  Fields  of  force  become  regions 
where  there  is  not  an  equilibrium  state  of  the  radions  and  a  flow 
of  radions  takes  place  to  matter  or  electrical  charges  in  these 
regions.  The  process  is  so  fine  grained  that  we  must  consider 


98  FUNDAMENTAL  PHYSICS 

this  picture  as  saying  the  same  thing  as  is  done  in  speaking  of 
forces  and  force  fields.  The  advantage  of  either  view  is  at  pres- 
ent a  matter  of  convenience. 

The  wide  applicability  of  many  of  the  laws  of  classical  me- 
chanics in  the  electrical  and  radiation  world  also  seems  to  indicate 
that  these, laws  apply  to  the  whole  realm  of  energy  changes  of 
radions  just  as  the  electrical  laws  apparently  apply  to  the  whole 
electron  realm. 

According  to  one  form  of  elementarquanta  theory  it  follows 
that  no  atomic  vibrator  can  absorb  energy  except  in  units  of  size 
hv.  A  diatomic  gas  cannot  absorb  energy  from  molecular  im- 
pacts unless  the  energy  of  these  impacts  exceed  hv.  It  begins 
to  absorb  when  the  energy  exceeds  this  value  and  this  absorption 
increases  rapidly  with  rise  of  temperature.  The  atomic  vibrators 
of  C12  and  Br2  begin  to  do  this  at  low  temperatures  because  the 
intraatomic  bonds  are  weak  and  their  frequency  values  are  small. 
The  fact  that  H2  acts  like  a  monatomic  gas  below  60°  absolute  is 
explained  on  the  same  basis.  Dulong  and  Petit's  law  of  the 
equality  of  atomic  heats  and  Kopp's  law  of  the  additive  proper- 
ties of  atomic  heats  in  compounds  have  been  interpreted  by 
Boltzmann  as  being  due  to  the  fact  that  atoms  of  solids  may  have 
natural  periods  of  vibration  and  that  these  atoms  are  in  thermal 
equilibrium  with  a  gas  when  their  mean  vibratory  kinetic  energy 
is  the  same  as  the  mean  translatory  energy  of  the  gas  molecules. 
The  energy  content  of  an  atom  of  a  solid  would  therefore  be 
twice  that  of  a  monatomic  gas  molecule.  The  fact  that  elements 
of  low  atomic  weight  such  as  C,  Bo,  Si  at  ordinary  temperatures 
and  many  other  elements  at  low  temperatures  behave  abnormally 
is  explained  by  some  on  the  elementarquanta  theory.  Linde- 
mann  has  obtained  the  relation  between  v  and  the  melting  point 
T  of  any  substance,  its  atomic  weight  m  and  its  atomic  volume 

]T 

2 

mv^ 


The  approximate  validity  of  this  formula  is  favorable  to  the 
quanta  theory. 

The  limit  of  visibility  to  the  eye  is  about  a  sixth  magnitude 
star  or  about  0.003  microlux  while  a  surface  becomes  invisible 
when  its  luminosity  is  less  than  4(10)~10  candles  per  square  cen- 


THE  THEORY  OF  ELEMENTARQUANTA  99 

timeter.  The  minimum  flux  of  light  perceptible  to  the  eye  is  about 
8.5(10)-14  lumen  or  1360(10)-12  ergs  per  second.  The  potassium 
photo-electric  cell  approaches  an  efficiency  equal  to  that  of  the  eye. 
Planck's  energy  quantum  is  3.8(10)~12  erg  for  the  frequency 
0.58(10)~15  of  maximum  visibility.  The  number  of  quanta  re- 
ceived by  the  eye  when  receiving  the  minimum  visible  light  is 
about  360  per  second.  Any  instrument  a  thousand  times  as 
sensitive  as  the  eye  should  indicate  discontinuities  in  the  light 
emission.  It  seems  that  the  selenium  cell  would  be  sufficiently 
sensitive  to  indicate  variations  of  this  kind. 

The  explanation  of  the  atomic  heats  of  solids  has  been  ex- 
plained on  the  theory  of  agglomerates.  Benedicks  derives 
Planck's  law  on  the  assumption  that  the  energy  (W)  of  a  mole- 
cule of  crystallized  solid  is  equal  to  3RT  (the  energy  if  the  atoms 
were  free)  —  Wo  (the  energy  of  agglomeration  when  T  =  0)  -f- 
F(T)  (where  the  disintegration  of  the  aggregate  due  to  the  rise 
of  temperature  is  taken  care  of).  The  factors  influencing  F(T) 
are  cohesion  (a  vectorial  quantity  for  crystals)  and  thermal 
motion.  Assuming  a  formula  obtained  by  Langevin  for  the 
action  of  a  magnetic  field  on  a  paramagnetic  gas,  Planck's  law 
can  be  derived  without  recourse  to  any  quanta  theory. 


23.  THE  RELATIVITY  THEORY 

The  general  concensus  of  opinion  at  present  is  that  the  funda- 
mental facts  of  electromagnetism,  the  aberration  of  light,  and 
many  optic  phenomena  require  the  assumption  that  the  ether 
does  not  partake  of  the  motion  of  material  bodies  which  pass 
through  it.  For  example,  the  experiment  of  Fizeau,  in  which 
the  velocities  of  light  were  compared  when  going  with,  and  when 
going  against,  a  stream  of  water,  was  interpreted  by  Fresnel 
as  indicating  that  the  the  ether  was  in  part  dragged  along  with 
the  water.  This  view  was  based  upon  his  theory  of  refraction, 
which  assumed  that  the  ethereal  density  was  increased  in  material 
media,  and  only  the  excess  of  ether  was  carried  by  the  matter. 
On  any  resonance  theory  of  dispersion  and  refraction  there  is 
no  excess  density  of  the  ether  in  matter,  and  so  Fizeau's  experi- 
ment requires  a  stationary  ether.  The  theory  of  the  stagnant 
ether  requires,  however,  a  positive  result  in  the  experiments  of 
Michelson  and  Morley,  Trouton  and  Noble,  etc.  The  only 
satisfactory  hypothesis  to  account  for  the  negative  results  ob- 
tained by  these  observers  is  to  assume  that  the  dimensions  of  a 
body  parallel  to  the  direction  that  it  is  moving  in  the  ether  is 
contracted  by  an  amount  \/l  —  /32.  This  shortening  is  very 
small,  in  the  case  of  the  earth  moving  in  its  orbit  it  would  be 
about  6.5  cm. 

The  theory  of  the  foreshortening  of  a  body  in  the  direction  of 
its  motion  through  the  ether  is  justified  by  other  reasons  than 
that  of  explaining  the  negative  results  of  Michelson  and  Morley, 
Trouton  and  Noble,  etc.  The  electrical  forces  between  charged 
bodies  for  instance  are  modified  by  the  motion  of  these  charges 
through  the  ether.  Now  it  is  a  fundamental  theorem  in  elec- 
trostatics that  a  charged  system  can  be  in  equilibrium  only  when 
the  electrical  forces  are  balanced  by  other  forces.  If  the  inter- 
electronic  forces  are  ethereal  in  origin  and  subject  to  the  same 
laws  as  the  electromagnetic  forces,  then  the  Michelson  and 
Morley  experiments  afford  evidence  for  believing  that  the  inter- 
atomic and  intermolecular  forces  are  ethereal  in  their  nature. 
Lorentz  has  shown  that  the  electrons  must  themselves  undergo  a 

100 


THE  RELATIVITY  THEORY  101 

foreshortening.  Rayleigh  and  Brace  have  shown  that  there  is 
no  double  refraction  due  to  action  depending  upon  the  earth's 
motion.  This  implies  that  the  periods  of  vibration  of  the  elec- 
trons in  the  line  of  motion  must  be  equal  and  in  order  that  this 
be  so,  the  longitudinal  and  transverse  masses  of  the  electron 
must  be  altered  by  the  motion  in  the  same  manner  as  the  forces 
in  these  directions.  Neither  the  rigid  spherical  electron  of 
Abraham  nor  the  constant-volume  electron  of  Bucherer  satisfy 
these  requirements.  The  electron  of  Lorentz  satisfies  the  re- 
quirements if  when  at  rest  it  is  a  sphere  of  radius  a,  and  when 
moving  with  a  velocity  v  it  becomes  an  ellipsoid  of  revolution 
with  its  shorter  axis  in  the  direction  of  motion.  If  ra0  is  the 
mass  at  rest,  mi  the  longitudinal  and  m^  the  transverse  mass, 
then  mi  =  m0(l  —  02)~**  and  ra2  =  w0(l  —  02)~w  as  we  have 
seen. 

At  present  there  are  two  theories  which  attempt  to  explain 
the  optical  and  electrical  properties  of  systems  in  relative  motion. 
These  theories  are  the  Lorentzian  theory  of  a  stagnant  ether, 
and  the  Principle  of  Relativity.  The  deductions  from  the  two 
theories  are  very  similar  and  agree  with  many  if  not  all  of  the 
experiments  that  have  been  performed.  The  necessity  that 
gave  rise  to  these  theories  was  the  accumulation  of  the  unsuc- 
cessful experiments  to  detect  the  earth's  motion  through  space 
by  its  effect  on  terrestrial  phenomena. 

In  the  theory  of  relativity  there  are  two  postulates.  The  first 
postulate  states  that  the  uniform  translatory  motion  of  any 
system  cannot  be  detected  by  an  observer  in  the  system, 
making  his  observations  on  it  alone.  In  other  words,  any  law 
or  any  theory  deduced  from  any  set  of  laws  is  the  same  for  all 
systems  between  which  there  is  no  relative  acceleration.  Ordi- 
nary experimental  laws  hold  until  the  relative  velocity  of  any 
parts  in  a  system  reach  (10) 8  cm.  per  second.  Such  a  system 
may  be  considered  as  quiet  and  for  it  the  Newtonian  mechanics 
will  apply  approximately. 

The  first  proposition  assumes  that  the  velocity  of  light  is  a 
magnitude  that  is  "physically  infinite"  so  that  the  addition  or 
subtraction  of  finite  velocities  does  not  change  its  magnitude. 
This  condition  is  a  sort  of  definition  similar  to  the  absolute  zero 
of  temperature  and  the  use  of  the  velocity  of  light  as  an  infinite 
quantity  may  be  interpreted  physically  as  being  equivalent 
to  stating  that  it  is  impossible  to  give  any  material  particle  a 


102  FUNDAMENTAL  PHYSICS 

velocity  equal  to  that  of  light  just  as  it  is  impossible  to  cool  any 
body  to  the  temperature  of  absolute  zero. 

The  main  object  of  the  Principle  of  Relativity  is  to  establish 
a  relation  between  the  laws  of  a  quiet  system  and  those  of  a 
system  which  is  moving  relatively  to  it.  This  Einstein  was 
able  to  do  by  introducing  certain  propositions  that  do  not  con- 
cern the  laws  of  any  quiet  system.  In  the  theory,  space  is 
considered  homogenous  and  three-dimensional.  Time  is  homo- 
genous and  unidimentional.  This  means  that  the  transforma- 
tion of  space  and  time  coordinates  between  systems  that  are  in 
relative  motion  are  linear  transformations.  It  is  also  assumed 
that  it  does  not  matter  upon  which  system  an  observer  may  be 
situated,  the  measured  relative  velocity  between  two  systems 
will  be  the  same.  The  word  "stationary"  is  only  a  relative 
term  and  anything  that  can  be  said  about  a  moving  system  with 
reference  to  a  " stationary"  system  (by  definition)  can  also  be 
said  about  the  "stationary"  system  with  reference  to  the  moving 
system. 

The  second  postulate  becomes  necessary  when  it  is  required  to 
determine  when  two  events  occur  simultaneously  in  two  different 
systems,  a  quiet  and  a  disturbed  system.  A  method  of  making 
comparisons  of  this  kind  is  to  send  light  signals  between  the  two 
systems.  It  is  then  necessary  to  make  assumptions  as  to  the 
space  velocity  of  light  and  the  second  postulate  of  relativity 
assumes  that  the  velocity  of  light  is  independent  of  the  relative 
velocity  of  the  source  of  light  and  the  observer  and  is  always 
constant  in  a  homogenous  medium.  / 

The  further  development  of  the  Principle  of  Relativity  is 
mainly  a  mathematical  one.  The  results  are  somewhat  as 
follows.  Suppose  LI  and  L2  are  two  quiet  systems  whose 
relative  velocity  is  v.  An  observer  is  situated  in  LI  and  has 
instruments  for  measuring  x,  y,  z2,  t ,  P,  Q,  R — where  P,  Q,  R  .  .  . 
are  certain  physical  quantities  that  may  be  functions  of  the 
coordinates  and  the  time.  A  similar  observer  in  L2  measures 
corresponding  quantities,  xr,  y',  z,  t' ,  P',  Q',  R'  .  .  .  .  The 
known  laws  of  each  quiet  system  give  relations  of  the  following : 

f(x,y,z,t,P,Q,R,  .  .  .)  =  0.    f(x',y',z',tr,P',Q',Rf,)  =  0. 
From  the  Principle  of  Relativity  it  follows  that  the  relations 


THE  RELATIVITY  THEORY  103 

between   the   coordinates  are  as  follows,  /3  being  the  ratio  -,  c 

c 

being  the  velocity  of  light  in  space. 


Or  -  vt) 

VT^J>'  v'  *' 


('-?) 


The  laws  or  equations  of  electromagnetism  are  simply  rela- 
tions between  the  coordinates  of  certain  so-called  rigid  bodies 
referred  to  standard  frames  of  reference,  time  as  defined  by  clocks 
and  certain  electromagnetic  processes.  One  of  our  first  problems 
is  that  of  defining  time.  Our  judgments  of  time  depend  on 
determining  the  simultaneity  of  occurrence  of  two  events.  "A 
friend  leaves  the  house  at  four  in  the  afternoon,"  simply  means 
that  the  leaving  of  the  house  by  this  friend  happened  at  the  same 
time  that  the  hour-hand  of  the  clock  pointed  to  four.  The 
question  of  simultaneity  is  not  a  difficult  one  when  the  events 
happen  in  the  same  place.  When  the  events  happen  at  a  distance 
from  one  another  it  is  no  longer  an  easy  matter  to  say  when  two 
events  are  simultaneous.  The  relations  between  the  time  recorded 
in  two  systems  is  given  under  the  section  describing  units. 

In  order  to  define  when  two  events  are  simultaneous  (for  it 
has  been  shown  that  the  coincidence  of  two  events  depends  upon 
whether  the  observer  is  moving  along  with  the  system  or  not), 
it  being  possible  for  two  events  to  be  simultaneous  when  regarded 
in  one  coordinate  system  and  not  being  simultaneous  from  a 
coordinate  system  moving  with  respect  to  the  first,  Einstein  has 
defined  two  widely  separated  clocks  A  and  B,  as  being  together 
when  the  time  required  for  light  to  pass  from  A  to  B  (TB-TA) 
is  the  same  as  the  time  for  the  light  to  pass  from  B  to  A(TfA-T'B). 
Under  these  conditions  the  unit  of  time  of  a  "moving" 
system  appears  longer  to  an  observer  who  considers  himself  to  be 
"stationary" — and  the  leading  clock  is  behind  time.  The  unit 
of  length  in  the  "moving"  system  appears  shorter. 

Local  time  according  to  Lorentz  is  the  time  measured  by  a  set 
of  observers  who  are  moving  uniformly  in  a  straight  line  relative 
to  a  standard  set  of  observers.  The  relation  of  local  and  standard 
time  is  a  reciprocal  one,  the  local  time  of  one  set  of  observers 
being  the  standard  time  of  the  other  set  of  observers,  and  vice 
versa. 

Proper  time  (Eigenzeit  of  Kowski)  is  defined  for  each  particle, 


104  FUNDAMENTAL  PHYSICS 

and  may  be  considered  as  the  age  of  the  particle.  When  a  par- 
ticle is  in  motion,  its  increase  of  age  depends  on  the  increase  of  the 
standard  time  and  its  velocity.  If  the  particle  is  moving  uni- 
formly, the  increase  of  age  is  equal  to  the  increase  in  local  time. 
The  age  of  a  particle  will  thus  depend  on  the  nature  of  its  path 
and  upon  its  velocity  while  traversing  this  path. 

In  the  case  of  linear  translation  we  have  seen  that  this  can  be 
transformed  away  so  that  no  trace  remains.  The  transformation 
that  does  away  with  rotation  alters  the  equations  of  relative 
motion  in  a  definite  manner  indicating  that  its  magnitude  is  a 
physical  constant. 

As  regards  gravitation  let  us  consider  the  acceleration  a  of  a 
gravitation  field  in  the  direction  of  a  coordinate  Xi  such  that 

dzxi  ' 

-jTf  =  a.     Introduce  new  variables  xz,  tz  such  that  a  =  0  and 

then  -j-rj  =  0  and  we  would  describe  the  appearance  by  saying 

there  was  no  gravitation  at  the  point.  The  Einstein  view  of 
gravitation  is  somewhat  like  this:  in  a  space  free  of  gravitation 
and  other  forces  a 'material  point  describes  a  straight  line  and  in 
xyzt  space  its  "world  line"  is  also  straight  defined  by  gij.  Intro- 
duce gravitation  and  the  definition  (gij)  of  the  world  line  (still 
straight)  becomes  more  complex  and  involves  functions  of 
(x,  y,  z,  t).  No  arbitrary  constants  are  involved  and  gravitation 
is  made  a  property  of  space.  As  the  xyzt  space  is  the  vehicle 
of  all  physical  phenomena  so  these  must  all  be  affected  by  gravi- 
tation. There  are  ten  gij  coefficients  and  only  six  equations  to 
determine  them.  Four  conditions  can  therefore  be  arbitrarily 
chosen.  Were  there  ten  equations  there  would  be  an  absolute 
space  and  time. 

The  relativity  theory  appeared  after  a  long  period  during  which 
scientists  had  agreed  to  consider  length,  mass  and  time  as  abso- 
lutely invariant  magnitudes.  As  long  as  atoms  were  the  eternal 
rigidly  material  bodies  that  chemists  believed  they  were,  it  was 
natural  to  believe  that  the  mechanics  of  rigid  bodies  was  a  suffi- 
cient explanation  for  all  phenomena.  The  relativity  theory  gives 
us  a  more  proper  view  of  length,  mass  and  time  as  magnitudes 
used  by  the  laboratory  rather  than  fundamental  magnitudes  of 
nature.  In  the  discussion  of  the  fundamental  units  (in  so  far  as 
our  experimental  knowledge  extends)  of  electrical  charge,  velocity 
of  light  and  energy  the  "relative"  theory  developed  from  the  use 


THE  RELATIVITY  THEORY  105 

of  these  units  was  found  to  follow  naturally.  There  is  therefore 
nothing  mysterious  about  the  theory  so  far  as  experiments  cover 
the  field.  When  we  try  to  exterpolate  beyond  the  region  of 
experiment  we  may  obtain  curious  results.  To  see  the  experi- 
mental application  of  relativity  let  us  consider  a  few  applications. 

To  describe  the  relativity  effects  introduced  by  laboratory 
conditions  let  us  consider  several  systems  in  relative  and  un- 
accelerated  motion.  System  1  consists  of  submarines  in  water; 
system  2  of  aeroplanes  in  the  air;  system  3  of  molecules  of  air; 
system  4  of  planets  in  the  ether;  system  5  of  electrons  in  the 
metals;  system  6  of  alpha  particles  in  the  ether;  system  7  of  elec- 
troethons  in  the  ether;  system  8  of  bullets  in  the  air;  system  9  of 
elementarquanta  in  the  ether,  and  system  10  of  waves  in  the  ether. 

The  laboratory  observers  in  these  different  systems  wish  to 
communicate  with  each  other  and  to  compare  their  standards 
and  the  laws  which  they  have  measured.  Evidently  the  condi- 
tions of  the  medium  must  be  such  that  they  know  the  laws  of 
the  medium  as  regards  energy  or  other  transmission.  The 
bullet  type  of  communication  for  example,  is  found  to  be  an 
accelerated  motion  for  material  media. 

The  condition  of  relativity  imposes  approximations  in  that 
the  means  of  communication  between  the  laboratories,  the  signals, 
must  first  be  studied  by  the  laboratories  before  their  units  are 
compared  and  under  conditions  that  may  be  local.  Consider 
aeroplanes  in  air  with  the  experimenter  exposed  and  using 
sound  as  the  signalling  means.  He  may  conclude  that  the  sound 
transmission  depends  upon  the  direction  of  the  sound  and  of  the 
aeroplane  flight.  If  he  encloses  his  laboratory  and  experiments 
with  sound  transmission  in  this  space  without  measuring  the 
air  pressure  he  will  find  the  velocity  of  sound  to  depend  upon  the 
direction  the  sound  is  measured  (provided  the  velocity. of  the 
aeroplane  and  his  altitude  above  the  earth)  is  sufficiently  great. 

Let  us  assume  that  systems  1,  2  and  3  can  only  signal  by  using 
sound  waves  that  have  been  found  to  possess  a  constant  velocity 
S.  This  condition  we  can  imagine  to  be  comparatively  easy  for 
submarines  because  they  are  observing  in  an  almost  incompres- 
sible medium.  Systems  4,  5,  6,  7,  8  and  9  employ  light  waves 
whose  velocity  we  will  also  call  c.  Because  the  observers  are 
assuming  the  velocity  of  the  free  medium  to  be  constant  its 
velocity  could  be  used  as  a  definition.  Interesting  questions 
can  be  asked  whether  any  system  can  move  with  a  greater  velocity 


106  FUNDAMENTAL  PHYSICS 

t'han  c  through  a  medium  without  experiencing  acceleration. 
What  phenomena  takes  place  when  the  velocity  c  is  approached? 

When  referring  to  any  system  S  will  be  used — when  to  any 
particular  system  as  a  submarine  in  water,  *Si  and  when  to 
different  laboratories  (A,  B,  C,  .  .  .)  in  any  system  Sa,  Sb,  Sc, 
etc.,  or  to  any  particular  system  as  the  experiments  of  Michelson 
and  Morley  with  reference  to  the  relative  motion  of  the  earth 
and  the  ether,  S^a,  S&. 

As  regards  the  equipment  of  the  laboratories  it  can  only  be 
suggested  that  the  science  of  laboratories  has  not  been  advanced 
sufficiently  for  to  indicate  a  general  set  of  apparatus  and  units. 
Experiments  indicate  that  neutral  atoms  become  ionized  when 
their  velocity  is  increased  sufficiently  and  corresponds  to  the 
motion  of  ions  through  about  500  volts.  It  follows  that  appa- 
ratus such  as  clocks  are  only  adapted  to  conditions  where  the 
relative  velocities  are  small. 

Now  it  is  evident  that  the  laboratories  of  those  systems 
employing  sound  for  signalling  purposes  will  meet  very  peculiar 
problems  when  they  compare  their  experimental  data  if  the 
relative  velocity  of  the  systems  approach  that  of  sound.  Indeed 
if  the  relative  velocity  of  two  submarines  in  the  water  was  greater 
than  that  of  sound  it  would  be  impossible  for  them  to  communi- 
cate with  each  other.  The  problem  of  different  laboratories 
established  on  different  air  molecules  would  present  very  unique 
problems  too.  Here  we  would  find  sudden  changes  in  the 
velocity  of  the  laboratory  such  as  would  apparently  introduce  a 
"very  intricate  physics  "  for  molecular  laboratories.  An  electron 
laboratory  introduces  us  to  a  new  world  on  account  of  the  intense 
electric  field  about  the  electron.  Bullets  in  air  are  mentioned 
because  these  may  possess  a  velocity  greater  than  sound  and 
suggest  that  particles  may  move  through  the  ether  with  a  velocity 
greater  than  that  of  light. 

The  kernel  of  the  new  science  is  to  be  found  in  the  require- 
ment of  a  laboratory  meaning  for  all  definitions,  terms,  units 
and  laws.  You  speak  of  the  longitudinal  diameter  of  the 
electron  with  a  velocity  approaching  that  of  light.  The  attitude 
of  the  new  science  is  to  require  a  definition  of  the  above  terms. 
And  the  difficulty  of  doing  this  is  certainly  apparent  after  our 
brief  discussion  of  the  c  e  r  units  and  the  ten  systems  considered. 
And  unless  length,  time  and  mass  can  be  given  "laboratory" 
definitions  they  are  meaningless.  Many  of  the  " peculiar" 


THE  RELATIVITY  THEORY  107 

results  of  the  relativity  theory  are  thus  meaningless  because 
terms,  definitions,  units  and  laws  were  discussed  for  conditions 
where  laboratory  experiments  have  never  been  made. 

These  are  some  of  the  laboratory  fields  remaining  to  be  ex- 
plored. We  should  feel  cheered  that  the  discoveries  of  the 
past  have  been  so  rich  in  permitting  us  a  vista  of  the  whole 
history  of  phenomena  as  a  single  whole;  the  elements  themselves 
apart  from  our  minds  for  which  the  consciousness  of  space  and 
time  may  not  exist;  the  laws  like  Hamilton's  principle  that  con- 
sists in  a  relation  between  the  whole  system  of  configurations 
which  their  past  contains;  and  for  which  as  far  as  we  can  deter- 
mine the  future  and  the  past  are  interchangeable.  True  it  is 
that  when  we  reenter  the  laboratory  the  stern  sphynx  of  nature 
holds  her  secrets  hidden  but  the  vision  that  she  has  given  us  of  a 
possibility  of  comprehending  at  one  glance  the  world  line  of  all 
phenomena  in  a  generalized  "space"  of  the  fundamental  ele- 
ments of  the  universe  is  indeed  manna  from  heaven.  It  brings 
us  into  a  deep  harmony  wTith  the  Great  Intelligence  and  we  see 
in  the  way  our  efforts  has  rewarded  us  the  measure  of  our  image 
of  Him  and  that  it  is  the  duty  of  man  and  of  all  his  organizations 
to  be  blessed  by  the  fullest  communion  and  harmony  with  the 
Divine  Plan. 


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